I apologize if this isn't useful, but I played a lot of Minecraft back in the day, and I seem to remember that the login cookie check was only done in two places: the launcher, and in multiplayer (servers could request you send proof of a valid, unexpired login credential, and kick you if you didn't have one). The latter could be disabled server-side. The game itself would run fine indefinitely with an expired login (i.e. one not valid for multiplayer).

Perhaps someone with a better recollection than me can say whether that's how it worked, and if so, it would suggest you don't need a MS account at all - there are alternate launchers, even open source ones.