Best way is to stay at either the BC, YC, BCV, Swan, Dolphin, BWI or BWV and then walk "home" Takes less than 15 minutes to get back in your room after Illuminations, even if you walk slowly.
Next best option is to just forget about a fast exit. Buy a cup of coffee, soda or other drink/snack and find a bench to people watch. After the bulk of the crowds have trampled all over each other on the way out, you leisurely stroll to the exit.
FWIW, using this method, you will get back to your room only a little later than the "fast exiters" and you will be in a much more relaxed and happy mood. Try it sometime - you might surprise yourself! JMHO. YMMV.