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
You may be able to find a used Sony TA-ZH1ES within your budget.  It's a fantastic headphone amp with a really good DAC.  I have about a dozen headphones, many of them "high-end", but one of my favorite pairings is with my Sennheiser HD-6XX.  It doesn't support MQA, but the sound quality will be much better than what you have now and you won't miss MQA.

Of the ones you've mentioned, I owned the Mytek Liberty (not the II) and found it very analytical and digital sounding.  Its headphone amp is not close to the Sony.  The Bifrost 2 is a great value for its price, but no headphone amp and it also has more of a digital edge to it than the Sony.
It's a lot cheaper than what you listed, but I would maybe consider the Topping DX7 Pro.  It uses very good clocks (the Accusilicon).  Then replace the two headphone amp op amps with Burson V6 Vivid and you have your discrete output stage.
MQA is the last thing I’d worry about. My RME without MQA walks all over the DAC in my Bluesound Vault 2 comparing against MQA files and not and that was before upgrading the power supply.