Where can I find 1/2" thick colored acrylic?
Unless your customers require personalization of the game pieces, you might want to consider going to a mixed medium approach to your production.  Prototype your products with the laser cutter using an opaque laser safe high-density foam or any other laser safe media which comes in your desired thickness.  Then once your prototypes possess the desired shape/size, make a silicon mold of them and then cast them in clear resin.  That will free you from your height limitations and seriously cut down on your material costs, while still producing a transparent product of acrylic hardness.

By adding a vacuum chamber to your resin casting process, you can eliminate the embedded air bubbles which often diminish the appeal of cast products.  When fully degassed, clear resins can produce crystal clear transparency, totally free of embedded imperfections.

The best part is that you can mix powdered dies into your liquid resin, allowing for a full rainbow colors and shades.