Is it possible for you to fit short naps (~20 minutes) into your schedule? Supposedly, if you practice napping regularly without letting yourself go over time, you will eventually get to the point that you can fall asleep quickly and immediately begin REM sleep.
Assuming that polyphasic sleep schedules are at least as effective as monophasic sleep, one such nap should be worth about an 1h20m of normal sleep. If you can fit even one in, and stick to taking it every day, it could be hugely beneficial. If you can manage to slip three of them in, you might be able to totally counteract the effects of your situation (although people seem to have trouble adopting polyphasic schedules that are designed to fit their schedule, rather than their circadian rhythm).
Assuming that polyphasic sleep schedules are at least as effective as monophasic sleep, one such nap should be worth about an 1h20m of normal sleep. If you can fit even one in, and stick to taking it every day, it could be hugely beneficial. If you can manage to slip three of them in, you might be able to totally counteract the effects of your situation (although people seem to have trouble adopting polyphasic schedules that are designed to fit their schedule, rather than their circadian rhythm).