The hinges remained too bendy despite reforming. A big thanks to @TwinBlueChimera who suggested to expose them to sunlight to harden them further as they are a photopolymer resin.
Three 2 hour exposures to indirect sunlight and they are now noticeably stiffer and able to support the base mask, as well as mask+antlers, when resting on a surface without warping. The slight yellow tinge indicates they were exposed to sunlight.