Ive seen something similar with the french cleats. You could try having a couple of additional cleats spun 90 deg, spun opposite to each other, this would stop any sideways movement. It would take some giggery pokery to get them lined up.
Failing that could you slap a couple of bits of 2x2, fixed to the board, with a 10mm hole through at 90 deg. And fix tnut to volume and m10 bolt through 2x2 into tnut in volume. Done on both side of volume it would hold it. Not pretty.