It really ought to be opened up with the same reamer that it was originally chambered with, bolt closure between the Go and No Go gauges. That, for your sanity, if nothing else. If it isn't opened up, there probably won't be any harm as your brass capacity will be ever so slightly short of a standard chambering. But, it doesn't sound like you are able to chamber factory ammo, which even if you could force it, will just grow (the factory brass) in length over time. So, it sounds like you'd have to at least shoulder bump, if not aggressively full length resize your brass, just to get it to chamber.
My biggest question is what the hell is the seller ('smith ?) doing selling a used barrel that is short chambered anyway ? Did he tell you that up front ? The time that it would take to open this up is in the setup to make the barrel's chamber concentric to the lathe. It would probably take 5 or 10 minutes on the outside to open it up. But, the setup time could be 30-45 minutes. All in all, it could be done in an hour or so. Not a lot of time. If he told you about it being short before you bought it, then it's on you. If he didn't, then he ought to make it right. He could chase the chamber with the reamer outside of the lathe, but that's not real conducive to accuracy. How much are you into this barrel for ? If it's not a lot, I'd suggest buying a new blank and finding a 'smith that will do the job right the first time. BTW, did you send him any fireformed bras for him to chamber to ? If so, was that brass short ? If yes, then you may own this one....
Oh, and there ain't no way in hell I'd entertain the idea of bumping/resizing 400 rounds of virgin Lapua 6.5 CM brass, just to compensate for the short chamber. Hell, the brass is worth more than a new barrel blank.......right up until you start "fixing/resizing" the brass.