The Habsburgs are famously known for the incestuous family line. As such why not start this pattern a century earlier and have Frederick III marry his niece Anne. Yes, he would be 15 years her senior but Frederick didn't marry until he was 37. It would probably very bad optics if his nephew, Ladislaus, died under his guardianship (even if it was Leukemia) just for him to become the next king of Bohemia. On the upside though, Frederick and Anne would only be very distantly related (Albert II of Austria is Fredericks great grand father and Anne's great great grandfather) so the likelihood of poor genetic health of their offspring is low. He'd be next in line for the Bohemian throne and for Luxembourg. How would the Albertian line of Habsburgs owning Bohemia change history? Bohemia right after the Hussite wars was devasted and there was a lot of anti-German sentiment in the population but it was still wealthy and probably had a positive economic outlook. With a electoral vote, could engage in a lot more active role in HRE politics. Poland could prove a problem since they wanted Bohemia too but it is engaged in war against the Teutonics at that point to contest the Habsburgs. However, rather than Poland or on top of Poland, Philip of Burgundy could become a threat as IOTL he disputed Anne and her husband William of Thuringias rights to Luxembourg which they eventually gave up in 1469 after several battles. Would Philip still dispute Luxembourg if his enemy wasn't a small prince but the Emperor himself? AFAIK, Philip tried to be on good terms with the Emperor hoping to get elevated to Kingdom.
If the Habsburgs still manage to unify their realms on top of having both Bohemia and Burgundy, their realm would encompass about half the population of the German part of the HRE. Matthias Hunyadi bought the Stephens crown from Frederick IOTL which could easily result in a long lasting alliance with mutual benefit. Frederick was Matthias fiercest opponent and his support could result in a huge boost in Matthias' legitimacy. Likewise, without Matthias' help, Frederick would not be able to get on the Bohemian throne.
If the Habsburgs still manage to unify their realms on top of having both Bohemia and Burgundy, their realm would encompass about half the population of the German part of the HRE. Matthias Hunyadi bought the Stephens crown from Frederick IOTL which could easily result in a long lasting alliance with mutual benefit. Frederick was Matthias fiercest opponent and his support could result in a huge boost in Matthias' legitimacy. Likewise, without Matthias' help, Frederick would not be able to get on the Bohemian throne.