Two ideas suggest themselves, and a few caveats...
First, you can get cast acrylic sheets as thick as 2", but anything over about 1/2" gets really expensive; think $300-$400 for a 4'x8' sheet at 1/2". You should be able to span 2' safely with a 3/4" sheet, although I would be inclined to find a structural engineer to check on that...
Also, the joists can be laminated up from the same acrylic. You will still get some light distortion, but less of it.
The other thought is to cast the surface and joists yourself in one piece; a monoblock will eliminate a lot of the distortion effects, and be a bit stronger. Be sure to get a heat-resistant resin, and I would be inclined to add venting fans, too.
Bear in mind that you will scratch the heck out of the surface in no time; if it's thick enough, you can polish it out, but still...
Would your needs be served by building a stage, and putting acrylic panels around the edges to light through?
--Sam
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