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So many "buts" hinder the implementation, as it seems to me, although maybe I'm just a noob and don't understand?

I'm assuming something like setting the order of hero appearance from the very beginning of the game. If a class isn't suitable in the tavern, the next hero in order is taken, and the previous one is taken as soon as it becomes possible. Heroes bought by both players are tracked, and as soon as they both die/are removed, they are added to a random location in the list. If you want to prevent main heroes from being dug up, a hero who was a main hero for at least one player will not be dug up for everyone.
It's more complicated to connect this to the AI mechanism, but that's also solvable.