How much is too much? When should I quit?

I think a transfer to one main department sounds like the best move. Write up the request to transfer to Dept. A with all the key points of how it will benefit you, your life, and lastly, both departments. Make an appointment to speak with your supervisor about it; that way you'll feel less rushed. If they're unconcerned about your personal stress, explain how you truly want to put in your best work, and how you simply can't under such a heavy workload.