For holy orders specifically, members of the order could replace dynasty members. Maybe a special mechanic could be similar to the decadence mechanic, where you have to concern yourself with making sure members are proper representatives of holiness, like having virtues instead of vices. A decadent holy order could risk losing the right to be a holy order, could act as a game over. Or if you end up holding land, it could secularize and just become a regular feudal game, or nearby Christians could be given the right to take your land.

Instead of heirs, maybe a knight of the order can take on a squire/apprentice, so an order tree still fills out like a dynasty tree.

The biggest issue is I don't think there are any holy orders at the start of the game, and even then, they don't start with any land, so they'd essentially be designing a mechanic that wouldn't even exist at the earliest start date, and it's not like you can just start as a character and shift into a holy order when they do start, unless you're given the option to send a son or something and play as him.

It'd be a lot of time and work for something that would only become a major aspect centuries after the earliest start date.