I use this rifle for hunting and fun shooting off the bench, Bushfire. Like you, I find it too heavy for a match rifle; we shoot three rounds of 13 in a comp here, and I get fatigued with the RMH. I have a Pedersoli Tryon for competition matches.
It took me a while to get a good load in the RMH, but it sure was fun getting there. While it shot well enough with Pedersoli's recommendation of .535 ball and a .010 patch, I felt it could do better. I have finally settled on a cast 530 round ball and .018 pillow ticking spit patch (60gns of FFG Wano real black) . I also found a greased over powder wad tightened the groups too. I'm at a consistent two-inch group, centrally, at 50 metres. I say two inches truthfully, as sometimes I can shoot a clover leaf of five shots, but realistically more often than not there are two or three that get a bit out of centre. The lads who advise they are getting inch and a half groups with open sights and round ball at 100 metres leave me scratching my head
. I sure like shooting the Hawken when just relaxing, enjoying the pure joy of such pieces and the processes of delivering the shot to target.
That's a nice stable of arms you have there. My collection consists of the Hawken and Tryon, both Pedersoli 54's, and I have two Parker Hales as well, 1858 and 1853 rifled muskets (two and three band). These four keep me well satisfied.
Pete