I wipe between shots with a dampened patch, which I usually dampen with my tongue. These are flannel cotton cleaning patches, and I use one size( large) for all my guns. Simplifies storage, and ordering. The moist patch will clean the crud out of the grooves, on the way back out of the gun, while attacking any built up crud down at that the breechplug face. If it is very humid out, so that my cleaning patch comes out very gooey and wet, I will follow it with a dry patch. But, I go down half way, and then back it out about 1/3, then drive the patch down two thirds, and back it out and then put it down to the breech and pull it back out a final time. I found that allows the dry patch to mold to my jag better, and reduces the chance of it getting stuck.
If I do get a dry patch stuck, I simply pour some liquid moose milk down the barrel and wait for it to soak the patching. The patch comes out very easily after that, cleaning the bore very well. I then run a couple of more clean dry patches down to soak up any of the remaining cleaning fluid. My moose milk is made from Water Soluable oil, purchased from a local machine shop, Lestoil liquid soap, hydrogen Pyroxide,(drug store) and water. The HP goes in last, as it is the most unstable and tends to boil off. Other recipes use olive oil, mineral oil( Ballistoil) and even peanut oil, instead of the water soluable oil, murphys soap instead of lestoil. Just shake the container before dampening a patch, and you should mix the oil and water temporarily for your purpose.