I must say that your idea just doesn't sound the best to me. But I do hope that the black powder ammo you get is what they call "carbine loads" which have only 55 grains of powder under the 400 grain bullet. I also hope your rifle's trapdoor latch isn't as worn as the barrel and that you have had the gun checked out by a knowledgeable 'smith before doing any shooting. Further, if that carbine is not capable of accurate shooting, I wouldn't hunt with it at all.
Now, about cleaning, just clean the rifle like you would a muzzleloader. You will also want to clean the empty cases if you plan to keep them for reloading.
Pretty sporty when they start that "Self Cocking / Auto Ejection" stunt, ain't it ?
......The Block flying off always makes for an interesting story to tell, while squinting through your one remaining eye,...too.
You have given some GREAT advice here, Se�or.
The "Cowboy Loads" that I've scoped out were all OVER the place, in terms of alloy quality and hardness, with attendant variations in diameter. Probably not much of a concern in a barrel that likely started out new at a whopping .463-.464 in it's grooves.
Than and again, it might have LOTS of rifling, HIDING under a serious wash of old leading,....can we spell BOMB, yet ?
GTC