I'd lap them out. You can use a 22 case, but I'd use an unfired one,,not a fired case.'
The chamber is supposed to accept the unfired ammo case freely and that is what you are aiming for.

Pull the bullet carefully from a couple cases so as not to disturb the thin case mouth. Dump the powder. You still have live priming compound in there..

You can epoxy your 1/8 or slightly larger dowel into the case right over the primer in hopes that it deadens it if you trust that method and use the setup as a lap. But you'll be pulling the lap from the front of the cylinder.
You can fire off the priming compound, but I still wouldn't do it in the gun to avoid expanding the case any.

I simply soft solder a brass flat faced rod to the back of the case. Use that as the lap.
During the soldering process the priming compound fizzles off.
If it doesn't,,poke a lit match down the case once the soldering is done and it'll take care of it. The whole idea is to keep the case to factory unfired spec.
Wear eye protection of course.

Put the lapping compound very sparingly on the forward part of the lap and work it in the chamber. An older hand crank drill is nice for this but most don't have one. Even a bit-brace works very nicely for this chamber work.

Take it real easy if you use an electric drill to spin the lap and avoid getting the lapping compound to the rear of the lap and on the rim working that portion of the chamber over.
You can cut things over size very quickly if you want too especially using an elec drill and common valve grinding compound.