we also use a belt to actuate our arm, but we use a different technique.
you can see the belt in action
here My guess would be, like you mentioned, that your arm gets momentum and your motor stops too fast. We have a similar reaction when we cross the rock wall, the arm wants to go forward on the landing, but the PID keeps it in place, making the belt skip sometimes when the shock is too hard.
Putting more tension in the belt seems to make it better