Hey there! Eating disorders are a b****, aren't they? I'm experiencing a resurgence of bulimia due to taking too many classes at college this semester. It had been quiet for so long... Bleah! It's normal to feel sleepy or lethargic after you eat, especially if you eat a lot in one sitting. Nearly everybody gets that midday slump. It has to do with circadian rhythms in addition to the normal sleepiness after eating. I find that I'm very in tune with my body. If it doesn't feel the way I want it to feel, I interpret that as something negative and something to worry about or beat myself up for - even if what my body is feeling is perfectly normal.
I know what you mean by eating breakfast destroying your productivity in the morning. The same thing happens to me. It drives me nuts! I have a hard enough time waking up to begin with. I don't need a small breakfast putting me into a food coma. I eat breakfast, but I put it off for a bit and then just eat a little at a time.
I have had much the same food-energy cycle as you. My doctor let me take home a blood sugar testing machine to use for a week. I tested my blood sugar when I woke up, before eating, after eating, and before I went to bed. I also tested it when I felt unusually tired. All reading were within normal. My doctor suggested that I was simply sensitive to sugar and that I would benefit from eating complex carbs rather than simple carbs and to avoid refined sugar like the plague. When I follow those suggestions, I feel better. It seems that you're doing better eating no carbs. Perhaps I should try that.
(My sister-in-law's sister is studying to be a nurse, and she has found that people don't need nearly as much carbs as they currently eat.)
I really like quinoa, which is a seed, for giving me energy and calories without weighing me down.
Let us know how you're doing.