I just purchased a used Great Plains Hunter that's in really good shape. I decided to go with the Hunter because of the faster twist rate (1:28).
Dosen't the Lyman Great Plains Hunter have a 1-32 instead of a 1-28 twist? A friend of mine that I hunt with uses a .54 caliber GPH and all he shoots out of it are the Hornady Great Plains Conicals. I think he uses 90 grains of powder. It has a lot of thump because I've seen some of the deer he's hit with that minnie cannon.
So I would start with some Great Plains Conicals, some Lyman Conicals (anything but the Lyman Shockers.. the are junk!) and some T/C Maxi ball. You might also want to try some R.E.A.L. conicals.
I've been shooting my CVA Stalker Carbine with a 1-32 twist and so far 80 grains of Goex 2f, a lubed wonder wad, and a maxi ball and the accuracy is outstanding. Good luck with your rifle. Lyman makes a great one.