RE: Thompson Center Thunderhawk
They have a 24" barrel with a 1-38 twist. Also the breech plug is solid and does not come out as I remember. With that twist they shoot conicals and short sabots. I would try some 460 grain No Excuse Conicals, 460 grain Great Plains Conicals, 380 R.E.A.L.s, even some maxiball would be something to try. They should shoot well if you keep the powder charge between 80-100 grains of powder.
If you want to shoot sabots, try some 240 grain T/C Cheap Shots and see how they shoot. Load them with 85 grains of powder and see what happens..