I would drill the spinning nut until it falls then in that same hole I would uses some sort of anchor kind of like a drywall anchor or a jack screw or even a sheet metal speed nut or clip. I manged a Ace hardware for about 10 years there also sorts of blind hole solutions I would go to the local hardware store or auto parts and poke around in the nut and bolt section I am sure you can find something. Man I would use a rivot before I did all that work we use to sell aircraft rivets that where about the dia of that hole.with a push pin you drove down I have even seen black plastic ones.Heck you may not even need to drill just find one that fits.hope this helps.