If you're willing to perhaps damage JP finish, there is an automotive tool that might work. Don't know the actual name, I just call it a grabber. Mechanics use 'em to retrieve small dropped nuts & bolts from tight places. Best description I can come up with is a long tube, kind of like a lawn mower throttle cable with a thumb plunger on one end. Push the plunger, and a "grabber" emerges...spring steel, 4 claws that work kind of like the claws on a stuffed animal vending machine game. Release the plunger, the claws "grab" and grip. Might take several tries, but would probably work.
Ask at any auto parts store, a good parts counter guy would know what I'm talking about.