Looking at the pictures, it seems like you have a nice problem. If the dimensions are correct, I'd call it a wildcat, and just handload for it.

Since you mentioned the rest of the dimensions are pretty close, I'd suspect that means all of it is not quite a 7mm Mauser. I wonder if someone thought it was a good idea to neck the 6.5 MS up to 7mm. I think it's amazing that the bolt closed on the factory round. I'd think a full length sizing die could be made from your chamber cast, plus a backup cast to verify. Then, I'd be highly confident that a standard 7mm Mauser seating die, maybe a Hornady, could take care of that step.

Only thoughts. Very nice looking pair. I'm glad you're interested in shooting them.