This link (which looks reputable to me) states that REM usually occurs around 90 minutes after you doze off. I think that before trying the experiment, you should consider that you won't be getting any REM sleep at all if you actually sleep for the prescribed amount of time, which strikes me as very unhealthy.
Personally, this feels like a batch of psuedoscience, but I could be wrong because I've not actually researched it -- the link above and some similar things said in a sleep book I own are my only sources of knowledge.
Edit: This comment has been retracted. See my comment below.
The 90 minute thing for monophasic sleep seems to be true. I was a little surprised how regular my sleep turned out to be: http://www.gwern.net/Zeo
At the start of the night, down into light sleep, then deep sleep, then up to light sleep, and finally some REM an hour or so later. Regular as clockwork, practically every night.
Incidentally, an interesting link (well, it would be if people would post more of their data) is the Zeo sub-forum dedicated to polyphasic sleeping: http://blog.myzeo.com/forum/polyphasic-sleep-experiment-discussion/
My friend and I are starting the Uberman sleep schedule (six 20-minute naps spread evenly throughout each day) tonight. Have other lesswrongians experimented with alternate sleep schedules? Are any of you qualified medical experts who can give input or advice? Success stories and failure stories would both be appreciated, and I'll keep you guys posted on our progress.