I had the same problem with some thinner gauge strings (like 18g kevlar) slipping through the gripper no matter how much I adjusted the screw.
Solution: I put a plastic gift card in the gripper with the string. No damage to string and always works.
USPTA P1, 5x Head TGK 237.2, Technifibre NRG2 16, 55LBS
Gamma 2pt 6004 with Wise.