Considering the fact that the head of a Parker stock is a lousy design (Ever seen a bolt through the head of a Parker? Me too, about a thousand of them.) why would someone attempt a transplant? If the gun is an old one, and there has been any oil that made it's way into the head (more likely than not) you might simply be up against something not worth repairing to begin with.
I doubt you will be happy until you get custom dimensions in your measurements. I sure wouldn't do that with a Parker VH, but, you might.
Good Luck.
Best,
Ted