"The rifle has a factory barrel that has an enlarged terminal end that has a connector ring that you can feel when running a patch through it. "

What do you mean by connector ring? Are you feeling a loose spot when a tight patch is pushed through? I have a 1607 that shoots like crap (1 1/4" @50yd) but it has a loose spot right at the start of the larger diameter at the end of the barrel. Sounds like that is what you are describing. If that is the case, a new barrel is in order, cut off the offending portion if it will leave enough barrel length, or back-bore to the loose spot and re-crown. I will be trying the latter before replacing the barrel if that doesn't work.

Maybe all it needs is a recrown?