According to lots of bench-rest shooters, there is a much easier way. The magic ingredient seems to be Kroil- sold as a super-penetrating oil, "The oil that creeps." Instructions seem to boil down to this:
1. Use a patch wet with Hoppe's #9 or any other bore solvent, just to get whatever surface crud/powder residue it can get- then follow with a couple of dry patches Now you have a dry, semi-clean but badly leaded/metal-fouled bore.
2. Saturate a patch with Kroil, & push through the bore. Repeat. You want the entire bore well wetted with Kroil. Now, LET IT SIT. If it was mine, from what I've read I'd give it at least 2 days. And since it's a revolver, I'd wipe down the front of the cylinder & the underside of the top-strap, just above the barrel-cylinder gap, too.
3. To clean- more than one recommendation I've read(but remember, these guys shoot benchrest uber-accuracy matches & have a real phobia about damaging their $1000+ barrels) stresses that they never use a brush. Instead, they use a caliber-appropriate jag with a dry patch centered on it, that can be driven through the bore with only light tapping. According to them, after a few days of soaking with Kroil the lead begins to push out the opposite end of the barrel in sheets & strips!
But- if you don't have all that, just use a bronze/brass .22 cal bore brush- maybe wrap a little 0000 steel wool around it. Again, if it was mine, I'd do that, ck to see if it seemed completely lead free, & then- even if it looked pristine- I'd wet it good with Kroil again, let it sit another few days or even a week, & brush again.
Someone must have fired a Lot of rat shot to lead it up that badly. Whatever you do, let us know how it comes out.