Verdict (IMO, in case someone needed a cheap disclaimer):
For my music tastes, I prefer the spaciousness and aggression of the HE-4 over the musicality of the HE-500. I tend to listen to a lot of instrumental stuff, so vocals have never been something I long for. The HE-400 is still one of my "least" favorite headphones, it just can't compete against its brethren.
Great review man. The way you have them rated with the categories you used I agree with you 100%. Female vocals on the HE-500s are to die for. The instrument separation, air and imaging on the HE-4 are great. The HE-4 has the best air and space I've heard in the Hifiman headphones. Not to be confused with width and depth of soundstage.
While I have no experience with the Project Ember I'm wondering would the HE-6, HE-5LE or the HE-5 be a good match. As you go up in amps you will see how the HE-6 scales and separates it self from the pack, also the HE-5 and HE-5LE to a lesser level.
I like where you said the HE-500 and the HE-4s treble can go either way and the HE-400s treble is terrible (I said that). IMO the HE-4s treble extends more and has a better sparkle compared to the HE-500. The HE-4s can sound a tab bit bright depending on the DAC, but it's pretty true all the time. Unlike the HE-400s the treble can be all over the place.
I've found the HE-400s have a classic U shape with a mid rage suck out, while the HE-500 has a slight mid range hump. The others are pretty even with slight treble increases on some with some amps.