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Doesn't necessarily have to do with CoM being off to one side per se. I recall one guy a year or so ago had a battleship with a nice, deep CoM that was perfectly centered. His problem was that he had masts that went up about 20m above the command cabin. Cutting them in half removed the tilt for his ship.
So I would recommend looking at aesthetics like masts that are tall compared to the rest of the ship and see if removing them does anything to help.
Tilting when turning can be countered by using internal heliblades or under-side-mounted large props set to activate when you roll.
While turning is generally due to poor rudder-placement. Start placing them level with the CoM - that won't be perfect but is a good starting point for fine-tuning. If it turns into the turn (left turn -> left roll), place the rudders higher up. If it rolls out of the turn, place them further down.