Time may indeed be variable. But our models don't fly at near the speed of light...

The idea of scaling the environment is valid but the environmental aspect that needs scaling isn't time but the medium that the model is flying through. If we scaled the density of the medium that we should be able to maintain scale behaviour AND flying speed all at the same time. So all we need is a really big blimp hanger that's pressure rated for some multiple number of atmospheres of pressure. Or if the model was sized suitably to do this in water such that the density of water was at the same scale factor as air is for the full size we could fly the small model in a swimming pool.

Evan, there's already such compeititions. In scale comp's the judges award points for various maneuvers that are announced by the pilot before taking off. These maneuvers are graded firstly on successful completion and then the grading for points becomes higher for flying the model in a way that most closely appears to make the model look like the fullsize craft. Good pilots will learn what the maximum roll rate was on the full size and try to limit the model to rolling that fast. Same with the size of loops and turns.