Peter- moving the rear sight a bit one way or the other to centre the group is normal. Different loads will give different windage as well as elevation impact to the group. This is also normal. At 50 yards, changing ball diameter or patch thickness or powder charges can give up to 2" change in windage if my rifles are normal and I think they are. True, it is nice to have a load that "shoots centred" - sights centred on the barrel, that is. Round & centred groups usually show the ball is leaving at the top or bottom of the barrel's harmonic movement. Stringing vertically usually means the ball is leaving in the middle of the harminics or barrel whip and the different vertical points of impact are showing shot to shot velocity and pressure changes, which are also normal, where a little more or less powder usually drops the ball's departure at a high or low node in the harmonic movement. This is getting rather technical and ML's usually don't give this type of problem - but - they do shoow left or right with different loads.
Suffice to say, if you are happy with the accuracy, move the sights to bring the group into the centre. With your pictured group, a bit left with the rear sight, and file some off the front blade to centre the group and bring it up.
I knew a guy who actually was a really good shot. I didn't realize how good a shot he was until he sold his rifle and mentioned the sights. He didn't win much, as he was afraid to adjust the 'adjustable' sights on his rifle. It shot to the left right from the factory - so for 10 years or so of shooting rondy's he'd hold off for the impact error - of course, holding off for various ranges didn't help him to be as consistent on targets as needed. When he sold his rifle, he mentioned it shot about 2 1/2" to the right at 25 yards - always had - he'd never adjusted the sights to shoot centre. I like competitors like that - gives me a changce.