The extreme accuracy required for a TINY 8" mirror would vanish when that mirror was the size of the one on Mt. Palomar (the Hale 200") because the aperature would win and cancel the errors of the less than micro-correct surface. Even if it was only 50% accurate you would still get a whopping eye-full of astronomic goodness
I think you have that backward. A large mirror requires the same absolute accuracy as a small mirror, this why large mirrors are so difficult to make, why they ate so difficult to mount.
Have you ever made a mirror? You discuss correcting the polymer mirror as if were something new. The reason a glass mirror can be accurately made is the combination of the ability to accurately polish glass combined the the ability accurately test the figur/shape. The process of making a mirror involves many, many tests of the mirror as it progresses towards a finished optic.
Read the Perfect Machine, the story of the 200 inch. The final figuring was done in a temperature controlled basement. The optician would test the mirror, polish it for a few moments, and the let it cool for a week, test it again...
I suggest studying up on your solid mechanics as well as looking into the thermal properties of polymers. Study a bit of optics...
Put it all together along with realistic values for the material properties and then consider the effect of small thermal differences. An FEA program properly meshed would be the tool.
I am a big believer in KISS but I also know that telescope mirror is almost certainly the most precisely made object manufactured by man.
Most technical folks ate aware of a certain story with the punchline, "Well, I have solved the problem for the case of the spherical cow."
A real cow is a much larger job.