I’ll weigh in with my experience.
I have been using Swiss, Schuetzen, and Olde Eynsford black powder in the last three years. I have Goex as well, but have not used any amount of it lately. I usually use plain tap water that is cool to room temperature. At times I may spray some homemade “moose milk” black powder solvent into the bore but it really isn’t needed. I am using hooked breech barrels that I take out of the stock for cleaning. I put the breech end of the barrel in a small pail of the plain water after removing the nipple from the breech plug. Then put a patch on the jag on my cleaning rod and pump the water in and out of the entire barrel’s bore. I’m sure that is what you probably have been doing too. I try to do it outside or at least in the garage as it will have that Sulphur smell a bit like rotten eggs which can linger for a while. Then sometimes I change the water to clean and repeat. Then dry it with dry patches. WD-40 can assist in the drying by displacing the moisture. I have been using “Barricade” from Birchwood Casey for long term rust prevention. I usually check the barrels again the next couple days with a clean patch sprayed with Barricade. Most of the guys on americanlongrifles forum do it the same, just water and then dry it and protect the barrel.
Note: In my experience using scalding hot water in my barrels for cleaning usually produces “flash rusting”, I didn’t like it and won’t use it again, cool water works fine for me.
Moose milk is a mixture of: water, witch hazel, alcohol, and murphy’s oil soap.