Why not just order regular boards, cut the USB headers off with wire cutters and fill the ports with epoxy? That should prevent any casual thumbdrive usage.
The only hangup I see with that is that most boards don't have PS/2 anymore and you might need to connect a keyboard/mouse. To solve that you might need to epoxy a wireless transmitter into one of the ports and pair it with mice/keyboards as needed. But for situations where wireless devices are not allowable, I can't see any cheap solution short of soldering the USB wires to the motherboard. Damn USB for being so... universal.