Wow, in much better shape than I thought it would be. And yup, should be on the C&R list. I have my C&R 03 FFL and didn't see it listed specifically in the book, but know that it is because of the age. Looking at a $200 tax for transfer I guess.
You can probably score a lock cheaper on eBay, saw 2 on ther right now. I dunno the legalities on the locks, may require another $200 transfer (could be considered a machine gun by itself, no clue).
Really nice that you have the whole thing, doesn't seem to be missing any parts. Still on the stand, stand has all the parts, etc.
Certainly put a lot of care into cleaning it

I'd love to have something like that to restore, sure beats cosmoline soaked Turk Mausers.
It has a healthy coat of patina on it

Pics don't look like anything that can't be fixed though. I'm guessing that you'll probably have to have it blasted and reblued. On something like that, I dunno if I would go with someone local. There are people like Dean at
DGR who just do old stuff. May be able to find someone using the right message boards who has redone one. Try subguns.net to start. Lots of auto people over there who may be able to help.
It'll probably cost a lot to get fixed up, but when finished, probably looking at close to $20k in value.
And at say, a buck a round for good 8mm ammo, you'll be shooting $400 a minute
Freakin' congrats, nothing I like more than coming across pieces of history.