Getting comfortable with hunger

I have been following no sugar, no flour protocol, no snacks for 3 months. I have lost weight. I am now out of the prediabetic range (yay!). I am thrilled that it only took 3 months. My problem is this: I am still hungry, especially from 4-6 pm. and starting around 3 am. I am awake at 5 am ready to get up and eat something. Blood sugar is in the low ’80s. I thought I would be fat adapted by now and the hunger between meals would go away. Should I be eating more fat at lunch and dinner? (I did have a bona fide diagnosis of hypoglycemia years ago). Suggestions?