Recommendation Request: Headphone Amp/DAC combo

If I were in the market,with your budget & cans,I would get a Woo Audio WA7 Gen3 "Firefly", a pair of nice NOS tubes & an upgraded power cord & never look back...
If you absolutely want to blow the budget then either an iFi Audio "Pro iDSD" or SPL Audio "Phonitor XE"with DAC module would get my $...

I had been looking for an SPL Phonitor SE.

Have settled instead on a Lehmann Audio Linear II. Very well regarded.

Personally at that level I’d be looking at a separate amp and DAC instead of a combo unit. 

@mlapenta , I recently moved from a Cayin HA-3A to the Black Ice Audio Aries DAC/Amp/Pre, and am really happy with the performance it offers with a huge range of tuning options (channel balance, gain adjustment, independent left and right high frequency control, bass adjustments) and it responds very well to 6SN7 tube swapping. 

I could see this unit getting most off of the gear swapping merry-go-round in your price range. It should offer enough adjustment to dial in any headphone to your liking.