When I inherited my dad's Rem. 722 222 Rem. (First 222 Rem. that came to a dealer in Morgantown WV. about 1950.) It had accuracy problems to. Since the last Model 722's was made about 1963/64, When Remington went to the Model 700, Your rifle has to be 55 years old.
Dad's rifle shot 2" groups at 100 yds.
Dad's 722 had such a weak firing pin spring that once in a while it would allow the firing pin to come back in the bolt, The primer would pop the firing pin dent and smoke come back into the action. I pulled the firing pin out of a 700 and installed it in the 722, The rifle went back to less than 1" groups like it did when I shot it as a kid.
I got a short action 700 firing pin spring and Bill Talkington and I replaced the original spring. The 70 year old rifle still makes groundhogs lives in danger.
I would not worry about the barrel till you replace the firing pin spring and see what the old war horse will do.