It kinda sounds like the receiving threads are stripped, or that the bolt is not reaching the threads at all.
At this juncture I would try another identically threaded bolt that is longer just to make sure that the receiving threads are still good... But perhaps you don't have a lot of mounting hardware sitting around?
Also, do you see small metal filings falling out of the hole, or adhering to the bolt?
They were orange in color and that's the shade that was painted on the end of the screw.
All right, off to get a longer bolt from the hardware store, some duct tape, and the other type of allen wrench!
Will report back shortly