Leadnut,
Ammoniacal solvents, if left in too long, will etch steel and that is with chrome-moly barrels. From memory, which is a bad thing for me to rely on, ammonia is prone to attacking the sulphur in SS but I would not like to swear to that.
If I may comment on your second paragraph, the green on the patch, In That Instance, is verdigris, a result of the copper jacket material corroding. IMO, if your (copper) fouling is corroding, then your barrel is doing likewise, Under It.
I have no idea why green patches do not come out of your stainless rifle. The copper fouling in it should corrode too.