I doubt a lasting peace between Genoa & Venice was really achievable---bad blood and the commercial rivalry were just too intense.
I think that the pro Visconti faction in Venice would not countenance the destruction of the Venetian state, if GG or heir should be so inclined to work to conquer the Republic.
I would be curious as to what diplomatic correspondence between Venice and other powers at the time was going on to ascertain if Venice was indeed concerned by the rising Visconti power. Particularly with France. I could see a potential alliance there. You know, just in case...
Venice was certainly both dynamic and calculating enough to take at least some initial measures. Even at the same time working with GG so long as they had common interests.
The bad blood was there: the war of Chioggia was a war to the knife, and Genoa went quite close towin it (although it might have proven a Pyrrhic victory). However in the end Genoa lost, and badly: the really damaging outcome was not loss of land, but rather the loss of the skilled manpower which was the backbone of any fleet in the Medieval and Renaissance period: captains, coxwains, soldiers trained to fight at sea and so on. It takes at least a generation (if not more) to replace them when they are killed in a single battle or in a short war, and it is also the reason for which annihilation seabattles are relatively rare. It is an extension of the concept of fleet in being: galley (and even galeons) can be replaced fast enough, assuming there's money and naval supplies available; skilled manpower is a much more difficult thing to replace. This constraint applied even to much larger states: see the Spanish after Djerba or the Ottomans after Lepanto.
Anyway the point is that Genoa was ascendant prior to the war of Chioggia(also in consideration of the Hungarian pressure on Venetian possessions in Dalmatia and Friuli/Istria) but after the war of Chioggia they were never able to really compete with Venice on their own. I would also believe that the internal troubles of Genoa (which after the war of Chioggia was for more than a century either under the French thumb or under the Milanese one) stem out of the consequences of defeat.
Venice is somehow in better conditions, but also for the Serenissima the last 50 years have been a little bumpy and the victory at Chioggia came to a high price. Not to mention that the Turks are more and more aggressive in the Balkans and in the eastern Mediterranean, and the Hungarians are a problem to be dealt with.
IMHO there is an opportunity of arbitration and composition since both cities are somehow exhausted. Obviously it works better if the umpire has a big stick to wave (and Milan controls the inland commercial routes of both cities).
As far as the belief that the Visconti faction would not countenance the destruction of the republic, I think you give them morecredit than they are worth of. These guys would get to the top of the pyramid if Venice becomes a Visconti possession, and that would be justification enough, even discounting the pious drivel with which they are dressing up their ambitions.
While Venetian state was solid, and lasted for 1000 years to prove it, there were enough examples of naked ambition and conspiracies to believe that a new one could not be fuelled up by Visconti gold and promises.
Re Venetian diplomatic efforts, I'd point out that twice the French set upan anti-Visconti league: Mantua, Genoa and Florence were always in the game (even if their dedication was not always of the best); Venice never participated in these ventures.