I am experienced at DYI speaker builder. Many good suggestions on this thread.
1. The wrench could be stuck to the magnet. Be aware of buzzing or any unusual sound if the wrench stuck in the spider it could vibrate a hole in the woofer. I am not educated on the other drivers.
2. It would bug the heck out of me too. I would have to find it.
The magnetic pickup is a great idea.
Driver removal for someone experienced with that brand would be very helpful. If you cannot find the wrench and want it out of there a dealer might be able to help. Ask what the job would cost. I have had the same type of things happen that makes me feel like Elmer Fudd.