Since you are in Idaho and required to shoot conicals during the ML seasons i would look up BullShop bullets. Dan sells a large variety of muzzleloading bullets for around $50/100 delivered. Best to email him but he has a couple in the 400gr range that im pretty sure you would like better than the Great Plains. Traditions are often tight bored so you might need them sized a little smaller. My guess is about .501-.502
https://bullshop.weebly.com/blackpowder.html

Get some lubed wool felt wads to protect the base of the conical. Triple7 burns kinda hot and usually accuracy is better with a wad.

Triple7 can also leave a hard fouling ring near where the bullet and powder meet. Its called a crud ring and its produced after firing. You will probably need to swab after each shot with a lightly damp patch. Then a dry patch to remove excess moisture before reloading.