I have to agree with yeoman. Most my rifles that shoot black powder will also shoot Pyrodex RS. The degree of difference in shot placement would concern me. It will be interesting to see if going back to simple black powder makes all the difference. Now granted, there are rifles out there that are fussy about powder. I own a couple of them. But none of them would create the differences you describe.

I am sure your rifle is spotless clean before you start shooting. So that would not be a factor. Have you changed patches, lubes, or anything like that? I will be waiting for your next range session.