Okay, I have an alternative here:
D) Strike the "must not be immune to mind control" requirement entirely. Rationale: There's no such thing as "truly immune to all mind-control" in the D&D rules; the closest it gets is "immune to spells with the mind-affecting tag," which doesn't include all spells that produce effects that look a whole lot like mind control, as previously discussed.
I think "being able to list creatures like, e.g., the zodar as FBS" outweighs the downside of "might have to list amnesiac Zeus."
However, since I genuinely believe that a creature like the zodar (normally immune to mind control) is a possibility and amnesiac Zeus is not, please put me as voting for that option only in an "if option B is defeated" contingency.