Jake, when I read your post I got a bit confused because you referred to the Precision Plastic sheet that Ozark is selling as “board.” It is 0.030 in. thick sheet, which appears to be vacuum formed, as you said. FYI, this is the same stuff formerly made and sold by Precision Plastics of Lewiston, N.Y. which is near Niagara Falls. I think they were allowed to make it there because at one time that area was like chemical plant central (can you say, “Love Canal?”). Anyway, Ozark appears to have bought the rights to this product. As mentioned by some of the guys, many of us “glue” this material to styrene sheet, probably about 0.100 or 0.125 which is about 1/8 inch. This is pretty stiff, but even so the styrene will bow without bracing (I use 1/4- inch square styrene strip). BTW, I believe the reason the styrene sheet bows is because of the dissimilarity in the expansion rate of the thin Precision Plastic sheet and the much thicker styrene underlayer. In other words, the top layer shrinks while the bottom doesn’t, so it pulls up on it and ya got yerself a bow.
The guys here mentioned various cements. I use Weld On 16, which comes in a tube, is syrupy and take a few minutes to dry before it sets up. I don’t know about Amrbroid, but I would be careful what I use because some “glues” will eat plastic. BTW, these are not really glues, but solvent cements that essentially “weld” the plastics pieces by kinda causing 'em to melt together.
I try to apply beads of Weld On all over the sheet, kinda zig-zagging until I have laid enough of the stuff to ensure that somewhere along the line, some of it will stick to the raised areas of the Precision sheet, which, as you mentioned, is uneven. I guess you could keep spreading it on until you covered the entire surface area but that would be tedious. And, as I have found, if you get too much on in one place, it will start to eat the plastic sheet. To me, the perfect way to attach Precision Plastic sheet to styrene (or anything else) would be to use this plastic sticky tape (the name escapes me, but it’s something with Red in it), which Jack Verducci once wrote about in Garden Railways. It comes in sheets and ain’t cheap. But it will stick forever, and because you would be able to cover the entire area, not just those random spots where you laid down a bead of glue, you would be sure of prefect adhesion.
As for Precision Board’s resistance to dents and such–I don’t know if something like hail would hurt it, but if you take a swipe at it when you’re working on it, you can dent it. I know. I’ve done it.
Sorry to be so repetitive, but I had to get my two cents worth in. 
