Dr. Claudio Stampi at Harvard is the "go to" sleep consultant for many of the distance solo sailors (Vendee Globe race etc.) He can train guys to take 20-40 min REM naps that total about 4 hours of sleep a day, and they race like hell for 27,000 miles at high function over 90 days.

Alternatively, you could Red Bull it. Hey, I think i just found a potential sponsor!!