I have never had to use anything but cool or cold water, whether I was shooting oiled or greased patches, bullets of whatever - cold water works fine for me - no soap, no solvents, no brushes, just
water. Pumping in and out with barrel breech submerged in water. Been doing this since 1977 or so, after reading Holland and Holland's (33 Bruton Street, London W1J 6HH) letter to Wil Thompson
about the proper care of his antique side by side black powder shotguns and rifles- used with oil and greased patches and wads.
If you are getting residue from oils and greases, perhaps your patches are not tight enough. I go no buildup of anything except for some powder fouling buildup in the breech where the patch or
lubed bullet does not touch. That comes out with cool or cold water.