A: This is the sort of problem that, seen safely from afar, can seem vastly amusing. There must have been a dozen sitcom episodes based on this premise - all hilarious, I'm sure. In close-up, however, as you now know, it's not funny at all.
I can quite understand why you've kept well out of it - but it seriously limits your possible courses of action. Realistically, if you're to make things any better, you need to get involved. It's no good going to management and asking what they're going to do about it. There's nothing they can do. Though probably blessed by management, the am dram club is almost certainly a voluntary venture launched by the staff - and only the staff can fix it.
What this means, I'm afraid, is that you and your other tormented colleagues need to join the club and start a movement from within to overhaul its constitution. Committees need to be formed, with members democratically elected by secret ballot. One committee - strictly one-person, one-vote, irrespective of company status - must become solely responsible for the selection of plays and the choice of directors. Directors are given sole and ultimate responsibility for casting.
I know all this sounds ponderously bureaucratic and all the things that an am dram club shouldn't have to be. But I can see no other way of keeping your Kenneth Branagh manque in his place and ending the spillage of club into workplace and vice versa.