I would recommend trying jsbs before you do anything else.
If you use a scope why worry about the dovetail? If you go to some of the muzzle loading build sites they show how to cut a new dovetail with common hand tools.
Before you go cutting the barrel, have you checked all the stock screws to make sure they are tight, and all at the same torque?? How about the scope mount screws, and the scope ring screws?? I would try all those first. If you find it shoots better, take out one screw at a time and put LocTite blue on them. Then let it sit for 24-48 hours to cure, then try it again. I'll bet it shoots a lot better!! Just my 2 cents as a tuner who has seen it happen many, many times. Good luck - Lee aka the "Shootist"
I'll buy it for scrap steel price if you get tired of fooling with it. Josh