I agree with steelslaver's recommendations all the way.

It's almost an easier decision when the fit is way off. You can jump right to machining the cyl and don't look back.

But I'd double check a few things first just for kicks before a final decision:

It's not uncommon that the barrel is not square on the back end. Is the barrel contact you observe on the 22 LR cyl completely around the chamber mouths? Or are they at the top, bottom or on one side?

If so, I'd true up the barrel end first with a stone and carefully hone it square by hand. This won't affect the bar/cyl gap with the original Jet cyl more than negligibly, and it should be corrected anyway.

Does the barrel rub all the way around the front cyl face? If not the cyl may have a little "runout" and would need to be faced off on a lathe to true up anyway.

__________________
Jim
S&WCA #819