Sub-$1250 DAC w/ built-in Headphone Amp


I currently have an entry level headphone listening stack, that I'd like to upgrade for both headphone listening, but to also include in a HiFi system stack when expanding my horizon to speakers. 

Currently have:
DAC = 'Ol DAC' from JDS Labs
Amp = Atom from JDS Labs

I am a bit overloaded with the options at this price point, but I know am looking for a smoother/richer sound from DAC as opposed to an analytical/etched sound. The following DACs come to mind - would any of you recommend one over the other? Source is primarily USB w/ Tidal MQA paired w/ HD58X Jubilee's.

- Mytek Liberty DAC II
- RME ADI-2 DAC FS
- DA-Art Aquilla II DAC
- SMSL M500 DAC
- Schiit Bifrost 2 (w/ separate headphone amp? or other multi-bit DAC?)
- Other?

Further - should I expect a substantial sound quality boost from my current set up?
uwrwilke
I say this only for the sake of the OP - I don't want to beat a dead horse. I was wrong again. It seems that the Mojo can function in a full-fledged pre-amp mode (not just fixed 100% output). Can someone who owns one chime in? I have one that should be here early this week.
It seems that the Mojo can function in a full-fledged pre-amp mode (not just fixed 100% output). Can someone who owns one chime in?


the mojo can be set for fixed or variable output (but not sure i would call it ’preamp mode’...)
My two cents...

TEAC UD-505. Dual mono DAC with w/unbalanced 6.35mm outputs,  1 balanced 4.4mm pentaconn and the ability to use in active ground.

The DAC is amazing f for its price and can upconvert 44.1k to 384k and to DSD 24.5mhz.

The teac can run fixed at 0db or +6db which 2 and 4 vrms each... solid set up. I love mine... us it can take a 10mhz master clock down the road for greater resolution and transparency. 
Ayre Codex. Bit more over your budget (isnt that the case for all of us) but unlikely to find a better dac-amp for less money. If you do, let me know...I tried.
If you're lucky enough to find one: Audio Alchemy DDP-1 + PS 5. I have this combo, it's quite amazing , and includes a preamp

or DDP 2 (Elac) , think 2nd gen