Tyler, Go with clamps directly over the "micarta" if you use steel plates.
If you bolt them around the perimeter they will still bow in the middle.....
I could always weld a rib across the top of the top plate.
The other thing I was thinking of was to use something like this:

a veneer press screw,
but I think I could cobble something up out of black gas pipe and threaded couplers for a whole lot cheaper, and it would still press down on the center of the top plate.
I also have a heavy duty vacuum pump which I guess the HVAC guys use to "boil" any water out of supply lines. So I could theoretically make a vacuum press, put the whole sha-bang inside a large vinyl bag, seal it up, then suck all the air out of it.