I assume you are shooting the rifle with the sights that's on the rifle in the picture, open sights and aperture sight.
If so maybe using shooting sticks from a sitting, kneeling, or standing position may be better then trying to shoot groups from the bench.
At least it may not be as punishing to you and your groups may be just as good as they would be from the bench.
I have a couple of old Savage 99's, (I know they are peashooters compared to what you are shooting
) I tried shooting them from the bench with the sights that came on them, as that's the way I'll be hunting with them.
The 300 has a buckhorn rear sight the 250 being the oldest of the two has a small rear sight plus an old Lyman tang mounted aperture sight.
I was not impressed with my groups from the bench with either rifle but was amazed at the things I could hit with both rifles from field positions.
I tell you this as you may find the same with your Sharps.
Anyway, I certainly wish you the best in your endeavors.