My personal preference is to zero check then fully clean and foul the bore with 1 shot before season, and then it stays loaded til I shoot at an animal or season ends. Then I usually forget to clean it until about spring, like now lol. My bore looks atrocious, but I figure what's it matter if it shoots well when it's fouled.
Are you shooting sabots? What cleaner are you using? I have found the Thompson Center No 13 bore cleaner to work really well if you use a lot of it, a sopping wet patch will usually dissolve most of the carbon on touch in mine. I've never used BH though, this is with Pyrodex or Triple7 residue.