If you want maximum consistency you should clean after every shot, especially while sighting in a scoped rifle. Some guns have a noticeable shift in impact points when firing from a clean bore as opposed to a fouled bore. The shift in your rifle could be negligible, or it could be an appreciable distance. Soap and water is probably the easiest patch wetting substance. You can also do a mix of Balistol and water (moose milk) which works rather well as a bore cleaning agent.
When it comes to real black powder and its substitutes, you're not going to be able to get off a long string of shots while using sabots. Some propellants are better than others, but they still are not as good as smokeless. As such with out a good lube to keep that fouling soft, you're not going to be able to get away from changing group size due to fouling.
When I take my nieces out shooting my old trapdoor springfields I always reload my ammo with a copious amount of lube cookies to keep the fouling soft. 54 grains of 3Fg powder, a piece of wax paper, 1/4" lube cookie, card wad, and top off with a 405grain lee HB. If there is a lube star at the end of the muzzle, you're doing right. We've shot 50 rounds straight with no change in accuracy other than the cold clean bore point of impact change as stated above.
Good luck to you. Oh, and BTW stay away from Pyrodex. I've caused myself more work in de-rusting BP firearms after learning that the cleaning I did was not clean enough.