Butterflies will definitely be an issue with moving the PoD back, though I think overall they can be kept manageable until we get into the run-up to World War II. Anschluss definitely gets more complicated with a strong Italy; Mussolini preferred an independent Austria, and only went along with Anschluss reluctantly. If a stronger Italy is more aggressive about defending its own interests, we could end up with an Italo-German war over Austria, which could get very interesting.
In The Long Night Falls, I solved the Anschluss difficulty by having Hitler and Mussolini make a mutually beneficial compromise in the late 1930s (alliance with Italy is more beneficial to Germany thanks to the PoD -early discovery of Libyan and Manchurian oilfields in late 1920s-, so Hitler is more eager to win over Benny's friendship, Mussolini is more ambitious, and Germany is the only partner that can help him fulfill those ambitions).
Italy gives its assent to the Anschluss while Germany recognizes an Italian sphere of influence in the Balkans and both powers agree to support their respective expansionist plans in Eastern Europe and in the Mediterranean. The two powers form a strategic partnership with an economic cooperation pact and a military alliance in 1937 and make a common understanding (later expanded to Japan on a looser basis) that joint diplomatic and military action was to be undertaken against common enemies if mutually beneficial to both sides. A side effect of this early alliance is that Italy espouses Nazi ideas about Lebensraum, to be applied in the Western Balkans and the Med.
The PoD makes Italy and the other Axis powers stronger: Those oilfields allow Germany and Italy to enjoy an abundant fuel supply before and during the war and Japan to defy Western oil embargo when it invaded China and later the Soviet Union. Mussolini develops the Libyan oilfields with the cooperation of American oil companies and is able to build up the Italian economy, military, and merchant fleet in the 1930s, as well as infrastructures in southern Italy and Libya. Germany is ensured an abundant oil supply from Italy. Germany, Italy, and Japan extensively develop their Navies and Air Forces and the mechanization of their Armies more than OTL, since they did not fear an oil shortage in wartime.
1938-40 main changes:
*Germany establishes the “Anschluss” of Austria and Italy annexes Albania in early 1938.
*At the Munich Conference of late 1938, Germany gains the Sudetenland and Italy gains Dalmatia.
*In early '39, Germany annexes Czechia, Italy occupies the Ionian Islands, Hungary annexes Slovakia with German-Italian support and joins the Axis.
(Japan achieves a draw in the Soviet-Japanese Border Wars of 1938-39 thanks to its own side of the PoD and butterflies).
*The Molotov-Ribbentrop-Ciano Pact.
*War starts with German invasion of Poland and Italian invasion of Yugoslavia.
The Wehrmacht swiftly crushed Poland, while the Italian Army toiled a bit more to defeat Yugoslavia, due to various flaws which the invasion revealed and that were ironed out, with structural reforms and German assistance, afterwards. Some licenses for German weapons and equipment were also traded to Italy to help the restructuring.
*The Winter War gives Germany and Italy a pretext to occupy Denmark-Norway and Greece respectively, while the Entente powers’ hasty intervention fails to deploy an effective resistance to those invasions.
*Germany makes a successful Blitzkrieg invasion of the Low Countries and France, Italian attack in the Alps front and in Tunisia is eventually able to make a secondary breakthrough, although made rather more difficult by French fortifications and troublesome terrain. Vichy regime takes over and makes an armistice with the Axis powers, by its terms the fascist powers occupied northern and southeastern France, Corsica, Algeria, and Tunisia. The British are able to evacuate and save part of their troops, although most of their expeditionary corps is trapped and destroyed.
*No Battle of Britain. Germany and Italy adopt a Mediterranean strategy, concentrating the bulk of their air forces and a sizable portion of their land forces in the Med, which is made possible by interwar infrastructure development in southern Italy and Libya.
*Joint German-Italian operations occupy Malta and Crete (albeit to a rather high price in blood), and overrun Egypt in late 1940.
*This prompts Spain and Vichy France to join the Axis and open their borders to German-Italian forces. Hitler and Mussolini are therefore able to land forces in Lebanon and Syria, and send their mountain divisions to besiege Gibraltar. Despite a valiant resistance, the Rock falls, sealing the transformation of the Med into an Axis lake, which was already ongoing owing to German-Italian naval victories and air theater superiority, the conquest of Malta, and the fall of Alexandria and Suez.
*Axis troops in the Levant open a second front in the theater that allows the Axis offensive to break through the Suez Canal and overrun Palestine and Iraq in early 1941. Pro-Axis Arab nationalist groups rise up to support Axis advance against the British (unsuspecting of TTL Mussolini's Lebensraum plans on the region). Turkey agrees to join the Axis. Stalin reacts to Axis occupation of Iraq and presence in Turkey with the Soviet occupation of Iran.
Main 1941-43 changes (although substantially influenced by the Japanese side of the PoD):
*The “Tripartite Pact” with Japan in early 1941. Japan agrees to join the coming attack against the USSR and leave South East Asia (and America) alone for the time being.
*Germany and Italy start an ambitious naval program for substantial expansion of the German and Italian submarine and surface fleets was started to secure naval supremacy in the Atlantic and strangle the British Empire into economic collapse. Portugal is invaded and occupied by Axis forces. The Italian military by now matches the German levels of effectiveness. The wide success of German-Italian military and economic cooperation persuades Hitler and Mussolini to establish a large degree of military and economic integration for the whole Axis bloc, so a large-scale system of Axis license-sharing, equipment standardization, economic cooperation, and joint military training is established, that aims to get the other Euro-Axis members (Hungary, Romania, Spain, and Turkey) close to the German and Italian standard. Vichy France is given a peace treaty and allowed to join the Axis as a full member in good standing. Such an ambitious military build-up makes it necessary total economic mobilization of Axis Europe.
*The Axis Blitzkrieg in the Soviet Union proves largely successful thanks to a more mechanized Wehrmacht, a powerful Italian expeditionary corps, Japanese blockade and later occupation of Vladivostok, Axis bombing of Baku which creates a serious oil deficiency for the Red Army. By end-1941, the Axis forces have conquered Leningrad, entrenched on the outskirts of Moscow and the banks of the Don, seized southwestern Iran, and repulsed the winter Soviet counteroffensive.
*America stays neutral.
*Spring ’42 sees a new Axis strategic offensive which targets the lower Volga basin. The benefits of the Axis cross-training and equipment standardization programs are showing their benefits as the increased effectiveness of the European Axis troops have come reasonably close to the one of Germans and Italians. The Soviet war effort is hampered by serious deficiencies of oil, foodstuff, other commodities, and industrial production which the trickle of American aid that manages to reach the Soviet shores can't make up for. After some months of fierce fighting, Axis troops occupy the lower Volga basin with Stalingrad and reach Astrakhan. The road is open for an Axis north-south strategic pinch to occupy the Caucasus and northwestern Iran, which further increases the oil starvation of the Red Army. Fighting continues in the fall, as Axis troops extend their control of the Volga basin upstream towards the Russian heartland of the Volga bend, conquer central Iran, and prepare for a great strategic offensive to take Moscow. A last-ditch Soviet counteroffensive sees initial tactical victories but is eventually contained and destroyed by Axis defense. In the Far Eastern front, the Japanese meet somewhat greater difficulties to make as dramatic gains as their allies; nonetheless they are able to exploit the growing disorganization of the Soviet forces and gradually conquer Outer Manchuria over mid-late 1942.
*Over late 1941 and 1942, the British gradually lose the Battle of the Atlantic. Repeated air-naval battles between British and German-Italian forces occurred in 1940-42 in the Med and the Atlantic which despite significant Axis losses (which prompted the revamping of the fighter pilot training system) gradually and severely deplete the ranks of the Royal Navy and the RAF faster than its Axis counterparts. Combined with the extensive Axis naval build-up, this ensures a significant surface superiority and a decisive submarine supremacy of the Axis forces in the Atlantic. The supremacy of the German-Italian submarine forces has substantial effects. German and Italian submarines roam up and down the Atlantic from a line of bases stretching from Norway to West Africa, with the support of Axis surface squadron task forces which issued on a regular basis. This ensures increasingly unbearable losses for British convoys and a steady loss of morale for a nation already demoralized by an apparently non-stop three years’ row of disastrous defeats. The growing Axis naval advantage is also increased by the loss of the Enigma trick for the British. The UK deciphering of Enigma codes had been lost when France had joined the Axis and it had given hard evidence of the intelligence breach to the Germans. The Wehrmacht has since plug the leak by adopting the slower but more secure Italian ciphers. Over 1942, Britain is rapidly nearing the point where its war economy would be crippled by a series of commodity deficiencies and the ability to supply garrisons in India and South East Asia critically compromised.
*In spring ’43 the Axis war machine seals the fate of the Soviet Union when two great pincers strike both north and south of Moscow and successfully close the circle around the Soviet capital, which falls after a month of desperate fighting. The Axis forces are able to occupy all territory west of the Volga. The loss of the Moscow region and the Russian heartland means the death knell for the centralized Soviet state machinery, which falls into chaos. Soviet organized resistance collapses and the Axis forces press on towards the Urals. The Soviet regime is overthrown by a military coup and Stalin and his inner circle shot. A nationalist junta government takes over, establishes the Russian Federation, and engages in the desperate attempt to fend off chaos and restore some sort of order for the unoccupied former Soviet space of Siberia and Central Asia using local resources. Organized military resistance (but not strong partisan insurgency) to Axis forces de facto cease, while Axis troops occupy their planned final positions on the western edge of the Ural Mountains and river. On their part, the Japanese stage a general advance and occupy Outer Mongolia and the Russian Far East up to Lake Baikal and the Lena River.
*The Axis powes agree on a Japanese invasion of South East Asia in late '42, as long as America is left strictly alone. Japan declares war to Britain, and its troops invade Hong Kong, British Malaya, Singapore, and the Dutch East Indies, while Siam opens its borders to the IJA and became a Japanese satellite. In a few months the Japanese forces overrun Malaya, North Borneo, and the DEI. The British forces retreat to Singapore, while the IJA invade Burma. A naval battle sees the destruction of the British fleet, albeit with heavy Japanese losses, and Singapore, long thought impregnable from the sea, falls after an attack from the mainland.
The Japanese clear British forces out of Burma. The IJN victory ensures the Axis a strong naval superiority in the Indian Ocean too, which the Germans and Italians exploit to conquer Oman and coastal southeastern Iran. India, wracked by nationalistc unrest, seems open to a two-front invasion, with the connection to Britain severed. In the Atlantic, the Axis naval war has progressed to an effective blockade and the British war effort can only really rely on the resources of the Home Islands, creating all kinds of critical deficiences. Air defense of the British Isles is staggering. The Soviet Union is clearly headed to a total defeat, and in America the perspective of intervention kept hitting into a seemingly impassable wall of opposition. In early '43, the situation has worsened to the point that the British morale meets a tipping point of frustration and demoralization. Successive war governments had been brought down by military defeats in early 1940, early 1941, and mid 1942. Now the fourth and last war government falls and the war coalition collapses as the British Parliament and public shifts from blaming the leaders to losing hope about the war. The peace faction takes over in Parliament and the new government asks the Axis powers for an armistice.
If Japan had not been influenced by its own side of the PoD, it is most likey that things would have turned up much like OTL in the Pacific, the USSR would still have been defeated (the availability of the Far East Land-Lease route and the lack of a front with Japan do not seem enough to reverse the other TTL factors stacked against it), the Battle of the Atlantic would have been initially favorable to the Axis and later to the Western Allies, Allied attempts to invade North Africa and Europe would have turned into bloody failures, and it is a toss-up whether the backlash from this failure would have caused a collapse of the will to fight in the Anglo-American public opinion, or the Allies would have won the war by nuking Europe.