What you are describing can happen even with a perfectly straight airplane, in which cas the culprit is spiral airflow.

The expensive fix is counter rotating props.

The less expensive fix is to decrease the incidence (drop LE; raise TE) in the right stab and increase the incidence of the left stab an equal amount. The AOA of the right stab dominates pitch behavior with left rudder KE, and vice versa. If the stabs are not adjustable, you can still make this "tweak" if the elevators use separate servos or a "Y" pushrod.

Moving the CG forward will tend to reduce the amount of differential behavior in the left and right KE.

Regards,