Bruce Gray recommends - wait for it - dry-fire with your eyes closed. After two months of doing so for fifteen minutes a day, I can safely say that that method will help work out perplexing shooting issues. Not watching the sights forces you to feel your way through a perfect smooth trigger stroke. Open your eyes afterward, and chances are the sights are pointing to where your off-center group usually goes. For me it's up - I seem to be heeling the crap out of the gun, especially strong hand/weak hand. Consciously focusing on the trigger finger and where I put pressure on the grip seems to have rubbed that problem out.
It turns out that one of the features of the Mosin-Nagant rifle is a magazine interrupter - the top round in the magazine is not under tension, and can move around enough to prevent rim lock. File that in the Things-I-Never-Thought-Would-Be-An-Issue-Until-Someone-Fixed-Them department.