I am left handed and my shots have a tendency to land to the right with semi autos, but not revolvers, including big bores.
I have swapped out the long trigger in one of my 1911's for a short style. We'll see if that helps.
I'm guessing it's anticipation. The first few shots are dead on, and after that, they will often slowly begin moving to the right.
Any other thoughts? I do plenty of dry firing with no movement of the sights. I've tried using both the pad and the joint of my trigger finger.
But I am like a green olive tree in the house of God: I trust in the mercy of God for ever and ever. Psalm 52:8