Responsive Design - Preserve Timing for Looping Animation

Stretching time changes the timing. If you have a looping animation and you create a mogrt, the easiest thing to do is to duplicate the mogrt as many times as you need to in the Premiere Sequence. The Protected region keeps the timing of that region from changing. The unprotected region's timing changes. There is nothing I know of that you can do to change that behavior.

All I can think of is to make a really long looping background animation, which you'd crop.  It's the time stretching that throws me here. 

In theory, if your loop is time-based, like a fractal noise with the evolution set to time*100, then that should always work, but when you time stretch it in a precomp, I'm not sure what would happen.  Can you pass the mogrt's duration from the parent timeline into the mogrt?  If you can, then you could control the final end animation via that instead of using an outro protected region.  Your Mogrt wouldn't be time stretched, just cropped to length and the loops would be unaffected.