So after some messing around this evening, my 44# @ 28" Thunderchild really seemed to like this setup:
.500 GT Trad cut to 28" carbon to carbon (8.6gpi) - 15gr insert w/250gr point for a total unfletched arrow weight of 524gr and an FOC around 25%.
If I stick with this, I think I'll have to experiment with some heavier inserts so I don't have to be stuck with finding 250gr broadheads.
I am still going to keep messing around, but I was pleased with this start. Thanks for all of the help and I'll continue to update as I get closer to a selected arrow.