Hi Paul, I guess the other guys are favouring a gyro. I suppose for the cost and the weight it is a good idea but If it was mine I would like to find the cause anyway.
Sloppy and flexible servo mount/linkages are the first thing to change.
The more solid the better.
How about 2 servos ? 1 either side? You could use small lightweight ones or is that too much hassle?
Jim