I'm not really a huge anime fan myself, but I've always counted Akira and Grave of the fireflies as two of my favorite movies. And I think you had something when you referenced David Lynch, whose movies I tend to watch over and over. With most Lynch, and with Akira, I usually get a map going, but I'm never quite sure where I end up. The last time I saw Akira, I really focused on one aspect:
Rebirth: and especially how rebirth is both violent and inevitable. At the end of the movie, Tetsuo becomes a giant, uncontrollable baby, sucking in energy and leaving complete destructiond. Add to that the psychic kids, who are the only people who have some sort of understanding of the whole thing. It seems like the younger the character, the more confused but simple the motivations are. The politician, the army man, the scientist, I get all of there motivations. But the kids, and tetsuo, they're somewhere else, but the scenes are about basic instincts, like protection, or fear, or intimidation.
There's definitely a tie-in between rebirth, and the failure of institutions, whether it be the orphanages, the schools, the military or religion. Possibly the misunderstanding of institutions on the messy inevitability of rebirth. How, whatever energy it is that tetsuo represents, these institutions are put in place to control or at least understand that energy, but are completely incapable of doing so.
By the way, I do love how emotional it gets everytime Grave of the Fireflies is even mentioned. I'm so glad you've covered it here.