Something else to note for single shot break open guns. I was having trouble with consistency with our encore some years back. I did a little research and a recurring theme kept popping up which is forearm/barrel contact. I checked my gun and the forearm was in contact with the barrel and frame in numerous places. After sticking a couple of washers in between the forearm and barrel at the screw holes and a lock washer in between the screw and forearm it pretty much solved that issue for my gun. It won't win any long-range competitions, but it pretty much shoots within 1.5 MOA now. Plenty good enough for me. I did the same thing for my H&R 444 marlin and it shrunk the groups on that as well.
Obviously your gun may just not like that round or that grain bullet but just wanted to relay something that worked for me.