Gp100
Yep, you got the dreaded .38 rings in your 357 chambers!
No big deal. Most everyone who owns and shoots 357s has to deal with it, and it's not that difficult to deal with. Start with a generous application of your favorite bore cleaning solvent (such as Hoppe's #9) & Let it sit for a while. After the solvent has an opportunity to soften up the fowling a little bit, run a few cleaning patches thru the holes and remove whatever portion of it will come out with the patches.
I like to switch over to a bronze bore brush at this point. You may have to make multiple passes with the bronze brush, and don't be shy about adding more solvent to help with the process. This should take care of most, if not, all of it.
If not, the next step is to get the power drill and chuck up that bronze bore brush in it. Lightly wrap the bronze bristles with 4/0 steel wool. Run the bronze brush back and forth thru the various charge holes in the cylinder while spinning it with the drill. A little more bore solvent can't hurt anything, if it seems appropriate. Follow up with fresh patches and solvent and then dry the holes with clean, dry patches.
That should do it.