How about a slightly different Mongol conquest? In Russia they had a concept of Vityaz, something like a warrior-monk (although also generally meaning "a knight" - not necessarily a member of "boyar" class, but more a medium-heavy armored lancer), and up until the battle at Kulikovo Field there were numerous instances of Russian monks taking up arms and fighting the invaders - Mongols included. Say, the Russians are bit more successful in repelling the Mongols around Dmitry Donskoi's time (1380s or so, if I remember correctly), however, the clergy ends up with much more power than in OTL, keeping these "Vityazi" as the special Orthodox warrior-monk order.
Therefore, the warrior-monks survive, and thrive due to ever-present menace of the Khanates. The Poles, Hungarians, and such adopt such practices since they are obviously successful, and form the Catholic version, that ends up subjugated to the Pope. How about this?