I actually drilled the holes out one size bigger than the engine mount instructions specified; I thought that this might be the root of the problem. To make a long story short, it worked to the point that the blind nuts went part way into the holes...and then, after digging into the wood just a tiny bit more than before, they started spinning around and folding up again. I may try to find blind nuts with short spikes--I've seen them on the shelves before, so I know they're out there.

Thanks for your help!
Jake