Will,
there is a definitve answer: Let the a/p fly until it proves its unability. The reason is: hand-flying in such high-workload-situations definitely segregates the 2 pilots: One is occupied flying, whereas the other has to handle all the system failures. So, very little redundancy for the trouble-shooting, if at all.
I had a chat with a friend flying the 747 (I have no recent Boeing Experience, I have to confess). What he says, that the similar procedure in the -47 keeps the a/p flying until disconnected by the crew. Any informed comment?