I have tried to figure out how to bbq a butt and either pull or chop then form in a patty...no success with this concept so far.
Perhaps debone a butt and form into a log, may have to tie it up like a braciole, rub, smoke, cool then slice to serve (reheat by frying in skillet)
Just thinking out loud
Sausage rounds will give you a nice presentation or depending on the size of the fattie it could accomplish the same thing. Rubbed sage works really well in breakfast sausage along with just salt and pepper. You can add a tiny amount of crushed chile pepper flakes for a touch of heat. Scrambled eggs for colour with seasonings on top and some neat style of potato. Something different, maybe shredded and formed into shap but not round like the sausage. Top it off with something green on the side.
Sorry just letting my mind wonder.