For my in line I use BH 209 powder and Thor all copper bullets. My cleaning process is the same as my center fire rifles. Also remember to clean your brushes and jags with break clean so they won't leave a false impression of a dirty barrel.
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I use the orange WW fluid. Works great for me, lately I have been using Shooters world Multi Purpose Black and it cleans up pretty easy.Any ever try windshield washer fluid?
Clean my cap locksx2 and .50 cal mtn pistol like that.......Hot water soapy Dawn and brush brush brush rinse with very hot water air dry the light coat of oil or better T/C Bore Butter.
DittoI've been cleaning my percussion cap the same way as this for decades. after the hot soapy water and running dry patches thru it I will then coat it with bore butter.
Inlines are easier to clean with the breachplug coming out, sounds like what you're doing is good enough. Just be sure to coat the barrel with bore butter or something similar before putting it up until next season or next time you shoot it.
Excellent Dawn dish soap and Hot Water….brushDitto