[dtengineering]

You could try using a carriage bolt. These bolts are designed for "blind mounting". In other words you drill a hole in the plywood and slide the bolt through before you put the pool noodles and fabric on. As you tighten the bolt from the back of the plywood it will pull the bolt in tight to the wood and there is a square shape on the shaft of the bolt close to the (rounded) head that will keep it from turning.

Alternatively you could try counterboring for a hex-head bolt and holding it in place with epoxy.... but the carriage bolt is probably your best bet.

Jason