I've thought of that, but IMHO the pressure points need to be at the
seams, not the faces, with V-shaped blocks, so that the pressure keeps
the faces lines up.

OTOH, I was thinking about servo-actuated clamps, so that the computer
can keep them in sync. I suppose a simple ring gear system, like the
supernove chuck uses, would work too. Sixteen jaw chuck anyone?
Maybe a longworth chuck? You'd need a top plate to keep the pins
aligned though.