Multilayer boards have a long lead time. Depending on what's important you might do both (time is more important than labor cost or money), or try to extract more information from the prototype before respinning (money is more important than labor cost).
That's pretty extreme though. I think I'd be inclined to eat an extra could thousand dollars or whatever to get rush service, and use some of the waiting time to come up with better procedures so that particular error never, ever happens again.
--sp