RC's got it right.
A couple issues here:
1. I wouldn't recommend returning the barrel as-is to the owner, with a live round stuck in it. I'd discuss this with the owner and cook that round off like RC said. That, in itself, won't do any further damage to the barrel than it's already sustained, but it will render it safe by eliminating the live round in it.
2. The barrel is very likely a lost cause...even if it turns out not to be damaged after removing everything, the labor cost alone is likely going to rapidly exceed the cost of a new barrel. And if the barrel is damaged in the repair efforts, which seems likely, then it will be wasted money as well.
Too bad the guy didn't just bring it in with the stuck round. Recovery from that would have been easy-peasy...cook off the round, remove the case, press the bullet out. Ah, well...live and learn, right?