I'm working on a 4 in 1 mail wristband as a gift, and I thought it would be interesting to try welding and brazing some rings. This is the result, prior to an acid bath and more polishing. Unfortunately I ran out of oxygen before I could get very far with the brazing, and I didn't manage to close a ring with the brazing.
I deliberately picked some 'worst case' rings, which had wide gaps. These were fairly easy to close, and I think that well-formed rings would come out very nice.
I wouldn't want to do more than a few hundred like this, but I think smaller pieces shouldn't be too bad.