Good point. However, since we're aiming for PLHC, it may happen so: Władysław III does not die at Varna, successfully keeps Polish and Hungarian throne and defends Hungary against Ottomans. They agree for a truce or even a lasting, while uneasy peace. Then, part of his Hungarian forces supports Poland against the Teutonic Order in 1454. Thirteen Years War happens as IOTL, only hardened in battle Władysław III with his veterans deals with the Order much quicker and easier than Casimir did IOTL. The days of the Teutonic Order in Prussia are over - Władysław, famous as champion of the Christiandom, is in much stronger position and decides to end Teutonic threat once and for all. Whole Prussia is incorporated into Polish kingdom, while the Order is given a choice - they get simply banished from Poland or they can settle on Hungarian-Ottoman border to help defend Christians from the Saracens. Of course Władysław fully intends to keep an eye on them so they wouldn't try to rebuild their power. Anyway, with Ottoman power at their door it would be much harder than against weak and divided Prussia. Some of the Teutonic Knights accept king's terms.
Meanwhile Casimir dies from some ilness, an accident, anything. Lithuanian magnats, still feeling threatened by Moscovia and Tatars, ask Władysław, Supreme Duke and strong ruler, to become their Grand Duke as well. And so we have a personal union between Poland, Hungary and Lithuania. Later it might evolve into Polish-Lithuanian-Hungarian Commonwealth.