[JesseK]

The simple and cheap solution may be to go with a higher pitch chain. I would think #35 at the smallest, but even higher may be necessary so the teeth of the sprockets have more chain to dig into as the whole assembly rotates.

I'd also recommend you fix the "holes don't line up" issue. It sounds like you have many lexan pieces and they all need to be identical. A jig, automated process, or assembly line may be in order. Look for defects as they come out of cutting/drilling and discard any grossly imperfect pieces.