I use and have always used boiling or as close to it as I can get water and laundry (1tbs/gal) soap.

The hotter the better.

Wear a heavy glove or use a towel to hold the barrel.

The brown coming out on a patch may be the "Seasoning" or otherwise burnt/baked on bore butter. Might not be rust.

After the hot water rinse, I also always run some alcohol patches in the bore to help rapidly evaporate moisture followed by dry patches and then Long Term Metal Protectant.

m2c

Tahquamenon