I agree with fintuckyfarms, I haven't seen any commercial operations using water culture systems use anything other than Styrofoam sheets. And just about every part of a
hydroponic system is made of some type of plastic (commercially built or home built). Sure some plastics will leach, but the general rule of thumb is to smell the plastic, if you can smell chemicals/solvents it will probably leach. But remember plants will only absorb what they want/need from the water. Just because something is in the water, dosen't mean it will be in the plant tissue/fruit. Remember the story a while back about the tomato farm in Australia that was destroyed. A pesticide was poured into the water supply, killing over 5000 plants ready to harvest. After finding out the plants were poisoned (and they stopped selling the fruit) the government tested the fruit over health concerns, and found no trace of the chemicals in the fruit.
It is up to you if you want to spend the money you can build your system using all food grade plastics. But there are people who feel even that isn't good enough like my mom who read a story somewhere, and now dosen't even want to use Tupperware containers to store leftovers in. However if you choose to spend the money for the food grade plastics, I don't think they even make a food grade Styrofoam. But you might try using cork. Like cork flooring. It's basically a wood flooring, but made from cork. Cork will float, but I'm not sure if it is a closed cell product and may absorbed moisture. However they use it for flooring, and wouldn't want it to absorb anything that may get spilled on it. So it might be a natural material that both floats, and not absorb moisture. You may want to ask some questions about it at places that sell flooring. However I doubt it will be cheep, and depending on the thickness of it, you may even need to double it up to make it thick/rigid enough.