First, 1:48 twist is slow twist designed for patched round balls. Forget the conicals in those barrels.
Actually, as has been stated, 1:48 is fine for conicals, and is considered the beginning of "fast twist". Slow twists (meaning they tend to not stablize conicals) is about 1:60, and slower. I have a 1:66 that tumbles conicals like a football kicked for a field goal, but my 1:48 barrels are tack drivers with T/C maxi-hunters. (I prefer the roundball myself)
The problem with some Traditions and some Pedersoli barrels, is they are rifled for black powder projectiles, BUT are made with modern machines. So..., you get very nice, crisp,
SHARP edges on the lands. If you cut the patching material as you load, it allows gas to creep around the sides of the projectile in an uneven fashion as it exits the muzzle. The uneven pressure nudges the ball just a tad..., so you hit ok out to 50 yards, but beyond, forget it. I had a Pedersoli barrel that made clover leafs out to 25 yards, and at 50 looked like buckshot.
You may need to take a few pieces of "green scrubbie" pot scrubber, and run them up and down the barrel with a cleaning rod, tight, to take the sharpness of the lands. Follow up with 4-0 steel wool and some water soluable engine valve lapping compound. Of course this is after you have inspected the patches, then inspect them as you go, until you stop the cutting.
If you're not cutting patches, and the patch/ball/powder combo is good, and you're firing from a tight position on a bench, then you need to have the crown on the muzzle checked.
Good luck.
LD