he reminds me of me a lot. i never recognized myself as being hungry before or during falling apart and then would get so hungry food repulsed me.
Maybe in addition to good food, you can work with him on recognizing when he's hungry. It took me a long time to learn to recognize that I was hungry WHEN I was falling apart, and too past hungry to want to eat. Then I started learning to recognize about 2 minutes before I was about to fall apart, and that I had to force myself to eat something. Now, (at 20), I know about... 10 minutes before I'm about to fall apart, that I'm hungry and need to eat NOW. (admitedly, I fall apart less drastically than as a child, but I still do fall apart). (and even then it's like, oh, I think I'll need to eat within the hour. And then 5 minutes later, I realize I have to eat something within minutes, and then sometimes if I'm out and can't find anything decent, I DO fall apart a bit. But I know to force myself to eat something.)
That said, be cause I eat more fat and less carbs, and because I make a concerted effort to eat regular meals and snacks (because I often don't "register" as hungry til AFTER I start eating), I don't hit "ten minutes before I'm going to fall apart from hunger" as often.
I think helping your son learn that "falling apart and not wanting to eat" actually means he IS hungry even if it doesn't feel like it, will help. I remember my mom telling me over and over again when I was falling apart, I know you don't feel hungry, but you fall apart when you get hungry, and need to eat. It definitely wasn't fast, but it helped over time.
For hypoglycemia, what I found worked (when I was younger) was a small bit of sugary snack (like a banana. banana was my food of choice to "make me hungry" or rather, realize I was hungry. I didn't want to eat it but I choked it down.), and then a nice snack of real food (which with what I know now, would include plenty of fat and protein. cheese is awesome.) the banana was somehow easier to choke down when food sounded disgusting, and gave a quick rush of sugar, which while not good for hypoglycemia, quickly made me feel truely hungry for some real food. It made me stop being crabby almost instantly as well.
Also you recognizing when he is getting hungry, before he falls apart and doesn't want to eat. He'll probably have signs (getting crabby, getting hyper, whatever).
If he's like me, the "reason he let's it get that far" is he may not recognize his crabbiness as hungry, and he may not feel himself getting hungry. I find that I'm not very in tune with my body in terms of bodily needs. I don't realize conciously (or I ignore it because what i'm doing is more interesting), until a bodily need is very very desperate, whether I'm desperately hungry, or have to run to the restroom. I imagine at 3, the world is much more fascinating and it's easier to get caught up, and harder to remember to pay attention to your body.
(on the eggs, I'm curious, does he not eat yolks at all? or not seperately? like do scrambled eggs have to be all whites, or just dishes where they aren't mixed? I always hated the texture of egg yolks as a kid, but scrambled eggs were fine. I think my mom overcooked the egg yolks. 6 minute eggs have a different texture and color yolks.)
HTH