HD800s : still, after many amps, on popular music (CDs), there is an vague/occasional sense of abrasion or piercingness (sorry to the English language) that can be annoying or tiring.
LCD3s: awesome bass with great texture with the right amps (tubed), but still it can feel like the music is pushing to get out, sometimes trying too hard. Still very pleasing and a keeper phone just a bit of an unnatural sound field.
HE500s: Spacious and one of my "goldilocks" phones, with all frequencies going to the limits w/o being overdone. Not as much texture as HD800s or Stax 009s, but more than enough to make it real and stay musical.
HE6: I believe it needs a good speaker amp and I have not had the privilege of hearing this combo but I sure trust Fang to make this sound great. So no judgement from me on this, and I assume you are right.