Typically I shoot one, or the other, in my 45/70 Trapdoor but never in 7 years have I used them both in same session. (AA5744 and a 405 gr bullet OR real BP, either 65 gr or 68 compressed, depending on the bullet)
Any reason not to follow up a BP session with some smokeless in the same rifle, after cooling the barrel and running a few patches down the barrel of course.
We're talking about a new Sharps 45/70 rifle.