A by-product like this totally makes me want to try polyphasic sleep again. I gave it a shot a year ago for something like 4 days, but I was just too sleep deprived to continue. I never got to the point where I could consistently fall truly asleep during the 20-minute window. A few times, but less than 1/3.
It used to take me 2-4+ hours to fall asleep on a normal night, but I've gotten it down to "only" about an half hour now. Meditation taught me how to deliberately disengage the verbal-thinking part of my mind, and for me it turns out that's one key to gaining some control over my sleep patterns. When I remember to do it, and not fall into my old habits anyway.