Well, I just got off the phone with the gunsmith. They bore scoped the barrel and based on the bulge say that it is not a candidate to be counter-bored. I sent a PM to the seller on the EE who had the barrel for sale and said I would take it. I am going to get the EE seller to mail the barrel directly to the gunsmith and hopefully with that I will end up with a properly working firearm. I'll be using this as a learning experience and being even more cautious when buying guns online...
I would have probed a bit as to why, e.g. bore is poor overall, but as long as the replacement barrel is very good, replacement makes sense if you intend to shoot it.
Keep the old barrel as it matches the rest of the gun (I assume).