Thank you for your interest in our laser cutting.
Unfortunately, we don't have much experience with machining plastics. Of the plastics we can cut, we have heard that PETG, Styrene, and ABS are easier to machine than acrylic. We can get PETG in clear, styrene in white or black, and ABS in white or black with one side smooth and the other side with a haircell texture. Here is what McMaster-Carr says about those plastics at http://www.mcmaster.com/#standard-plastic-sheets/=hc420l:
From what I can remember, 1/8" PETG, styrene, and ABS are not noticeably flimsier than polycarbonate, but if flimsiness is a big concern, please try purchasing samples from a supplier such as McMaster-Carr.
Please note that we normally get these plastics in the 3mm thickness (0.118" plus or minus 10%) rather than 1/8". We might be able to special-order 1/8" if 3mm will not work for you. Also, the laser-cut edges of PETG, white styrene, and white ABS tend to have a dark-yellow tint to them that might be hard to clean off. PETG usually comes with a protective plastic film that tends to peel off and tear easily so it doesn't completely protect the sheet from scratches, and styrene and ABS typically do not come with any protective film. If you end up ordering PETG from McMaster-Carr, you can make special requests to make sure they pick out a nice sheet with good protective-film coverage.
I hope this helps!