My thoughts on centering are that the pivot pin has little to with it. I have had little luck trying to peen one side or the other to get the blade to move to where it needs to be. I have had good luck by changing the inside surfaces of the scales to compensate for poorly shaped blades. I think that the blades centering is regulated by how the tang rubs against the inside surfaces of the scales. A little material removal down by the pivot end makes for a big change on the wedge end.
The wedge pin also plays a role in the centering, If you re-pin the wedge end it gives you a chance to slide the two scales back and forth thus changing their position relative to the blade.
Charlie