This picture includes the next piece of the finger and this is as well as the pieces will fit together.
This one shows down into the second finger piece and shows the conflict with the actuator and the finger piece.
This picture shows the under side with the three pieces assembled and shows the conflict between the gear teeth and the under side of the servo holder. The interference here will not allow the gear piece to move at all.
I hope that helps some.
I will work tomorrow on attaching the servo to the worm gear and getting the worm gear to rotate well in the holder.