the bolts included are #10-24 machine screws. I'm pretty sure the slots in the clips are too small for a 5/16", they're not much wider than the machine screws.
Instead of using the plugs I used 3/8" threaded rod with lock washers and nuts cut into 1-1/2" lengths. Then drilled 7/16" holes at 1/2" deep then epoxy in place . once set install clips.I feel its stronger since threads are embedded instead of a smooth plug
no special epoxy specified