From what I remember of a nearly new car that was crashed on a hillclimb, the wooden bits recovered their shape amazingly well, once the thrust of the bent chassis was removed.
I'd take advice, but my feeling is if one separated the chassis and straightened that, one might well be surprised at how well the tub comes back. Got a feeling that jigging a complete car is not a good idea for a Morgan, but I can't back the idea up as it is that, just an idea.