You' re on the right track mauser.

Shoot with a dry barrel. Dry patch out any bore butter or lube that' s in the bore before shooting that 1st shot...........that will bring it MUCH closer to the rest of the group. It might be off a " little" - but still close enough to hunt.

If you can take a full practice shot early in the AM or the day before without spooking the game that helps tremendously. If not, prime your flinter and put about 10gr of powder in the bore, hold it at a 45deg angle up and fire it.............this should create sufficient fouling for any subsequent shots for the next couple of days.