That's a funny little bump on the left channel at 3-4 kHz... I remember ohhgourami was suspecting there was a channel imbalance in his headphones somewhere. Maybe this is what he was hearing.

With your measurement the 10kHz hill does look pretty prominent (much more-so than Marv's plots). I guess that's the source of the brightness.

My by ear measurement of my fresh new pair, nearly match both yours and even closer, Purrin's.
Slightly lower in all resonant frequencies. Superb consistency in the line at the very least. In fact, it's possible my pair is better than either one measured here. This is with Lynx Hilo, needs every ounce of power to run HE-6, crossfeed and the eq and have 6 dB digital control headroom. (I like my digital volume control on the PC.)

Those headphones leave modded HE-500 way in the dust and finally are something that can compete with RE series of IEMs in terms of general quality.
(FR notwithstanding, even in case of RE-600, which sounds smoothly lowpassed - HE-6 are clearly superior there. Only my modded RE-400 can compete - yet lose.)

These are the first headphones I can say have correct air rendition. Though they are a tinge bright and the mids cut puts the presentation less forward and defined than ultimately possible, narrowing the center of the soundstage.

(In fact, correct in everything, inaudible distortion, correct decay everywhere - I'd have to compare against Audeze LCD-3, that might be competition. I don't have direct comparison on my hand, but from what I remember about Stax SR-007s, they lose against this due to bass. From memory, LCD-2 rev 1 pair I heard lose unequalized, but otherwise could be comparable.)

Bass thickness. It's not thick at all in the bass. I can hear a tiny bit of pad resonance, which should be fixable. I'd say reduced Jergpad mod, limited to pads only. Has to be carefully done so as not to conserve pad thickness - perhaps adding more foam to the inside of the pads.
Staxen actually have broken bass - large subbass cut - so I wouldn't compare to these. HD800 bass is inferior. Audeze bass may be superior, I'm not sure, but there definitely was less resonance.

Air - accurate equalization makes it perfect. HD800 sounds airier out of the box because it has smoother air - no dips - though it needs a flat cut. It also has a minor boost somewhere around those frequencies.
Seems like Hifiman made a tradeoff there in order to make manufacturing possible - and used a quarter-circle to dampen the front grillle reflection.
Said bit of foam also causes the 3k dip and it doesn't fully attenuate the 9k/12k resonances between face and grille. A better design is possible there - the correct material would be a much more tortuous with slightly larger pore size, attached to the grille in strips to not cover direct airflow. I'm not sure which material has such curly pores which are also large. Likely some kind of very loose fabric, I'd say low density blown PET absorber = low density multilayer microfibre cloth.