So I decided to abandon the heat-forming idea altogether. At this point, even if it worked I'd still have major problems implementing anything at a larger scale. Instead, I'm going with a cold, mechanical system based on the working-extremely-well nail system.
The first stab at a mechanical forming system looked like this:
The idea is that you just wind on some wingnuts to raise the tension and adjust the shape. And that actually worked pretty well to get the shape, modulo this being a first stab prototype. But the focus wasn't all that much better.
Finally, one might even say AT LONG LAST, the light dawned. I turned the mirror around and actually looked at it, searching for the distortions. Huh, they are right around those big holes I drill...OMG. The plexiglass just can't take the stress of the drill! I'm distorting the area around the hole! The oven is probably distorting the whole schmiel! That's why the nail version works so well. I'm just bending, not drilling or melting. What I need is some way of shaping into a parabola as non-destructively as possible. (I realize how obvious this sounds, but I didn't hear any Internet Geniuses suggesting it to me at the time, so bite me.)
Kind of fiddling around with it, I found that I didn't really need to shape the main body, so to speak, of the curve. Just pressing on the ends gave me a pretty good parabola. So, Mechanical Parabolic Mirror System Mark II:
Now winding on the wingnuts transmits compression to make the shape you want. I'm pretty sure that doesn't make a perfect parabola (I think it's actually a cubic curve, based on my skimming of some beam bending equations) but it's pretty damn close. Maybe not so close at full size, we'll see. If it needs more adjustment at larger sizes, I can add some tension non-destructively.
And how does it work, doctor?