I don’t have the wake at 4 a.m. sleep pattern, however I have experienced some of the effects you described. I noticed it while I was writing my magister thesis.
I had read all the information available related with my research subject and I had it all in my mind. I had a vague idea of what I wanted to propose but it was not clear at all. So I kept reading again and again the key articles I had found with this routine: I read a bunch of articles — usually 2 or 3 hours of reading — , then I went to sleep for 1 hour and then I wake up and write any good ideas that showed up in a mind map.
At the beginning I tough I was just lazy, or very exhausted due to the big effort I had made before. However with time I started to see that I was very productive during that period of time after waking up. I thought it was related with the sleep as the way for the brain to organize ideas and save into long-term memory. Your article adds another piece to the puzzle, the chemical substances in your brain released during sleep.
Nowadays if I’m trying to study something important and I need to learn it fast, I do that, read, sleep, keep reading or write a little bit about what I had read and repeat. As you said, it is ironic but for me, it is faster that way.