I had similar problem. I would wake up at 4 am. Then I at 8:00 - 8:30 I would feel sleepy again.
At that time, I did not eat anything sweet as it was suggested by Dr. Lam. I found an article by Ray Peat on Sugar etc. Basically, the article explained that Sugar is not bad. The next day I added honey to my tea (the whole day I was doing that). I slept really deep and soundly. I have sweets re-introduced into my diet since that time.