1-48 is a compromise twist, should do well enough with a patched ball [ of the correct size and with the correct patching material] and with the shorter and lighter conical and Minie' bullets.
1-28 is basically for longer and heavier conical bullets.
I have a .50 with 1-48 twist and have good results, less than 2" at 50 yds with open sights and a Lee REAL 250 gr conical bullet.
Try different loads, powders[ Pyrodex and 777], different amounts of powder, different patching materials and different lubricants.
Some thing may do well for you.