Why not use a bi-pod, after all, you can't drop that record book buck/bull at 350 yards and get in the Boone and Crocket record book unless you're real steady. Better yet, why not bring a portable bench with you when you go out. They're pretty light and will fit on the back of your 4-wheeler.
I used to have a bipod on my 22-250. Since both rifles are shooting about the same range - why not put one on a black powder muzzleloader.
Best wishes on your shooting
C F
ps Come on Randy, what is making that smoke coming out of your rifle in that picture.