So I got to spend the day with a forum member here in Los Angeles. Thanks @JoeyGun for inviting and hosting me in your home!
We had a mini meetup were I brought over my headphones (and a loaner HEDDphone, thanks @jb77) and we listened on Joe’s setup of a Chord Hugo TT2 feeding a Cayin HA-300. Joe’s Headphone is the Audeze LCD-3.
Joe’s got some pretty ‘snazzy’ tubes in his HA-300 (I forget the specifics, but I know the value of the tubes is several $k) and the synergy is his setup with his LCD-3 was pretty astounding.
The odd thing was that all but one of my headphones (Audeze LCD-X) sounded pretty bad. They were extremely bloated, and muddy sounding with a loss of detail and resolution (I was later told that my low impedance headphones don’t fair well with high impedance tube amps, which was evidenced in my listening).
The LCD-X however, exhibited a similar synergy and sweetness that his LCD-3 had. I was surprised since most headphones that are known to take tubes well are dynamic. The Focal Clear, and Lawton modded Fostex TH610 both exhibited extreme bloat. Very surprising was that the Air Motion Transformer of the HEDDphone yielded similar results; bloat and lack of detail.
When we switched over to the TT2’s output, all became well within the universe. 
They all performed well, as expected, but the stand out performer to my ear was the HEDDphone. Such a fantastic performer. Be it dynamics, speed, detail, and even tonality sounded spectacular. Where it not for fitment issues, and a lack of an amp to properly drive them, I’d jump on these in a heartbeat. That’s how much I enjoyed them.
After some electronics upgrades I definitely see a HEDDphone in my future.
The Focal Clear came in 2nd, with the LCD-3 followed by the Lawton mod (still waiting on some pads to correct them, as I feel these would actually place 2nd with the proper pads) with the LCD-X rounding out the group, to my ears.
We also hooked up my little RNHP and a/b/c’d the headphones which was pretty fun. The Focal faired the best on average, but the bigger take away was how well the TT2 performs. And though I prefer greater dynamics, I fully respect the TT2 for what it does. The staging is a bit exaggerated, and there’s some smoothing in the top end, but it’s such a pleasantly smooth listening experience. And I’d be happy with one myself!
As for the HA-300, I feel the tube options have been chosen specifically for Joe’s LCD-3 as that’s his sole headphone, and it’s been well tuned at that. I don’t know how, but even the planar timbre was improved with his tube choices, which was very interesting (incidentally, the timbre was also changed on the other headphones as well, albeit for the worse exception being the LCD-X). It added even more stage, and sweetened the sound with the right amount of honey flowing between the notes. I would’ve liked to hear the rest of the group on a less specific tube pairing, but that wasn’t in the cards that day. I definitely look forward to hearing more tube amps in the future.
Joe’s looking to upgrade to an LCD-4 and I can totally see (hear) why.