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
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.
First, I’d recommend dumping Tidal and getting Qobuz — it’s cheaper, sounds just as good (and some say better), better user interface, and no need to worry about MQA and all its silly unfolding BS. I dumped Tidal and am much happier with Qobuz. And I’d highly recommend the Soekris 2541 R2R DAC that also has a headphone amp (just make sure it has enough juice for your ‘phones). These multibit DACs tend to have a smoother, totally richer sound that you seem to be looking for. Hope this helps, and best of luck.