I'd use screws and epoxy. Epoxy alone might be strong enough but you will have no doubts if you use both. Since you're planning to use thick plywood you can countersink the screws that go into the old blind nuts and use pan head screws like the ones on this page to assure no interference:
http://www.microfasteners.com/catalo...ts/MSCMSPP.cfm
Most hardware stores should carry these and sell them individually versus buying a box of 100. Around my area you can get them at Home Depot, Lowes, Handyman Hardware. I'm sure there are lots of other sources in the area but these are all within a few miles of my house.