Since you've got no trem arm anyway, can you screw the claw at the back right in to bring the bridge right down into contact with the guitar - i.e. no float. Then you should get much more stable tuning. Slacken the strings before you do this, then tune up afterwards.
Since you've got no trem arm anyway, can you screw the claw at the back right in to bring the bridge right down into contact with the guitar - i.e. no float. Then you should get much more stable tuning. Slacken the strings before you do this, then tune up afterwards.