My sheet of UHMW was nicely planar, but it had small grooves in concentric arcs left by some sawing or milling covering both sides. I thought it would be a good idea to make the working surface as smooth as possible, so I tried sanding it. No dice! One of the properties of UHMW that makes it attractive for its many uses is extreme abrasion resistance - it out-wears steel 10 to 1! It should be planable, but I only have a mini hand plane, so that didn't work very well. Then I thought I might be able to smooth out the grooves with a propane torch, like finishing ice. Bad idea! The process did work somewhat as intended, but it also slightly discolored the surface and, worse, caused major warpage! It turns out that UHMW has some pretty strong internal stresses originating from uneven cooling at production, and those stresses result in warping when it is heated near the melting point.
I tried to flatten the piece by heating the whole thing up and then letting it cool slowly while being held flat by heavy things. Unfortunately, it didn't work. In hindsight, I should have just left the grooves. I doubt that they would have been much of a problem in the first place.
I decided that having a flat piece of plastic was important enough to warrant buying a replacement, so I took another trip to Colorado Plastic Products to rummage through the scrap bins. I couldn't find any UHMW scraps of the correct size this time, so I settled for some HDPE. I'm pretty sure it will work just as well for my application, and it is quite inexpensive.