All in all, yours is a pretty tall order, I'd opine! To find everything you want in one attractive, storebought package is likely to be
very expensive or of dubious quality and thus perhaps of dubious lifespan -- and still fairly expensive.
Is a kit a possibility? If you're in North America, perhaps Bottlehead. For better or worse, ASR has, I believe, tested at least one Bottlhead headphone amp.
The highest quality audiophile tube amplifier kits for headphones since 1995. Our kits pair great with AKG, Beyer Dynamic, Sennheiser and more. Made in USA.
bottlehead.com
Cosmetics are a bit bare-bones, though, without significant end-user intervention.
Does Elekit or Kits4Hifi offer any headphone amps? I don't know...
Most cost-effective option is pure-play DIY (or a bespoke build by someone who knows what they're doing) to get what you want.
I hear you
vis-a-vis "curvy tubes"*
Has anyone ever built a headphone amp using the 1626 tube? Many years back, Bob Danielak designed a low-powered loudspeaker amp (ca. 750 mW per channel), the "Darling", around the (at least then) cheap and plentiful - and curvy - 1626. Many others and Danielak himself have built variations on the Darling amp; e.g., my friend and hifi fellow traveler Joseph Esmilla:
jelabs.blogspot.com
View attachment 340525
(photo from the link above)
A 1626-based headphone amp would seem to me to be a (potentially) promising application of an interesting but limited power tube.
Food for thinking, as an old boss of mine (for whom English was not his first language) was wont to say.
_________________
* curvy 2A3s in my venerable Bottlehead Paramour loudspeaker amps (3-ish watts per). These are my backup 2A3 amps -- but now I'm getting down into irrelevant weeds.
ahem. Pay no heed to the small discs on the loudspeaker cabling
Those are the infamous
Mad Scientist Audio Black Discus free trial version tweaks!
They really and truly were
free (mailed in an envelope from New Zealand to me on their dime), so I was
happy to try them.
http://www.madscientist-audioshop.com/blackdiscus.html (link provided solely to practice good scholarship, and for information and entertainment purposes
only.