| | Full sleep cycle or no?
I too am a bi-phasic sleeper. I've found that the general assumption of a 90-minute sleep cycle (incl. REM) works for me. My current setup is 3 or 4.5 hours at night, with a 1.5 hour nap in the late afternoon. I find that I'm groggy for 10-20 minutes after each sleep session, but I spend the rest of my day more refreshed than before.
It appears that you are unintentionally taking a nap for a full sleep cycle (90 minutes, plus overhead for getting to sleep and waking up = roughly two hours). If you want to take shorter naps, you'll probably want to keep them real short in order to avoid REM. It's the in-between times that really make you feel unrefreshed.
Polyphasic sleepers swear by their ability to cram a full sleep cycle into a 20-30 minute nap. I've never tried it, but apparently a good bit of self-training is necessary to make that kind of thing work.