Polish-Lithuanian Commonwealth inception - Was there a movement opposing a Jagiellon ruler from Lithuania to get on the throne?

by Khundes

In EU4, the Polish-Lithuanian Commonwealth begins as a personal union between Poland and Lithuania created by an event really early in the game (so right after the crusade of Varna). The game offers the Polish player the option to have the Lithuanian monarch rule over Poland as well (and for it to become his primary title), but the player can also reject this and opt for a local noble to ascend on the Polish throne instead. Was there any such historical movement that opposed the Lithuanian monarch to rule in Poland, and if so what where they suggesting instead?

Madaboe

I am a EU4 veteran myself (2000hrs) but if you look into the history of the region it is actually completely different from what the game presents(you should really look into it). The Jageillon in the game is Casimir of Lithuania, who was actually the youngest and only brother left to the late Wladyslaw III. There was no real reason for the nobility to choose someone else.