If you superglue lots of drinking straws/popsicle sticks/thin dowels/whatever between a whole bunch of points all over such that the structure becomes entirely rigid, and then apply the epoxy very slowly in very thin layers with a very dry brush, over time, you might be able to do it. But that would probably take more time than simply rebuilding the thing in a heavier stock. And it still wouldn't guarantee that it wouldn't deform under the forces of rondoing.
Best bet is to consider this your practice run, and next do it for real. You know where everything goes and you know how accurate you have to be to make it work.