You could drill a hole through just one side and put a T nut on the inside (beveled side between the two pieces), then run an all-thread rod through it with a double nutted knob to open and close this.
You could also make the centers, where they join, rounded, as a pivot point for a bolt, and do the same thing. Might even be able to make the pivot point with additional holes so the clamp could be adjusted to up or down size it. Though that might be better done with two strips of metal, aluminum or hard wood.
Hmmm, I see more clamps on the horizon. Thanks for sharing.