As close as .311 and .308 are, the bore might just be a matter of deepening the grooves a bit. .321 might be a bit much for that, though, I dunno. People used to shoot .311 bullets through the old .308 bore Mini-30 all the time, and nothing blew up. Just wasn't as accurate as it ought to have been, I reckon.
My biggest concern is the chamber, though. I don't know what can be done about that other than:
1. rechamber to .30-40 Krag, which probably ought not happen because of the thin chamber.
2. reline the barrel and recut the chamber, which may not be able to happen (at least in .30 caliber) due to the thinness of the barrel. .25-30 or .25-20 might be an option there, though. I'd sure hate to go below .30 though...
I guess there isn't some way to fill the bad spot with some kind of super-special epoxy goo (or weld, though I can't see how that could be done) and then recut the chamber, eh?
Regardless, then there is also the issue of finding a gunsmith that can be trusted to do the work properly. If this gets screwed up, I can't just buy another one. I am not sure I have enough faith in any of the guys I know of around here to do any of this.
