This is where a large number of $1 hand clamps are most useful. To ensure this was strong enough (because obviously it needed to not only hold 6 sound chambers, but also house all of the mechanisms to move them), I first glued, then screwed. I had a drill already, but needed to get a new, smaller drill set to attach things from inside, as the old one wouldn't fit. The set I got are 12V Makitas (which is also what we use at Tinkering School LA), and I still love them.