I've been looking at the video a few times...
It's brilliant, love it, want one, no budget, will have to wait, darn.
... I can see a lack of rigidity/damping when it moves side to side, it kinda annoys me.
You could use triangular 10/15cm stiffeners in each corner (relative to movement) simple screwed in.
It would probably help precision.
Being a cheap arse, it'd probably cut-up old/defect PCB to make them...
G.