[Jared Russell]

Have you considered passive compliance (e.g., something deformable like foam or rubber) on the interior of your gripper? Then design your setpoint so that it is at a position which compresses your gripper to the desired effect.

Alternatively, if you don't mind stalling your servos, simply tell the gripper to close all the way (or close to it), and don't use an I term in your PID controller. This will effectively limit how hard the controller tries to drive the motors.