AI Blackboard is occasionally forcing my player character to use the AI's animation?

Debug it with animation debugging.
the AI should be instanced as its own thing, so even if you are changing a value that triggers the montage it should never interfere with a different instance.

Hard to say exactly where it went wrong, but I can confirm the setup works as I too have the AI derived from the player.
though, maybe, make a copy of the abim BP and assign it to the AI so that it is isolated.
this is usually helpful because the state changes occur differently when no user input is provided… you have to toggle a Bool or change a speed somehow.