Amp recommendations for Hifiman HE1000 V2

iFi Pro iCan 

I have the Hifiman HE400S so am somewhat familiar with the house sound, and if I’m you I’d be looking hard at the Singxer SA-1 amp. At only $599 it’s a fully balanced, Class-A design with plenty of power and exhibits the sound qualities you’re looking for, and you’d probably need to spend quite a bit more to get something significantly better. I believe your ‘phones come with balanced connectors so you’ll get the full benefits of the balanced design right out of the box.  Hope this helps, and best of luck.

Fantastic headphone, you will need a powerful amp to drive them to their full potential. An amp around 6 watts will get the job done, I use a Schiit lyr 2 a 6 watt tube hybrid to drive my power hungry HE560's a great combination. 

Good luck in your search..

Cheers Dave 

Hifiman made an amp that will work great with your headphones.  The EF-6 has 5 watts of class A power.  It's been discontinued, but if you look around you might be able to find one.

Didn't see a response as to budget, but since you spent on the  Hi Fi man phones, I expect you will want a comparable amp.
Also would help to know which DAC you are using.
But regardless, I would recommend the Linear Tube Audio MicroZotl.
It is an exquisite sounding piece & fits your sound profile.

Joyful blessings,
P.B.