Could you make the Pmma film on a liquid?
This was done for model aeroplanes of the "peanut" category, to produce wing films thin enough. They
let lacker dry on a liquid (water?).
Just find a liquid dense enough for Pmma and that does not dissolve it: Perfluorodecalin? As an alternative to the Pmma solvent, might you consider pouring Mma on the supporting liquid, and polymerize there by light?
If you can produce really thin film, this is very interesting for
Solar sails - a technology that looks a bit poetic but is a strong reasonable candidate for space travels shorter than now. There, the material of choice is polyimide.
http://saposjoint.net/Forum/viewtopic.php?f=66&t=2102&start=10#p40927A machine to make existing polyimide thinner thinner in a controlled fashion:
http://saposjoint.net/Forum/viewtopic.php?f=66&t=2102#p24358