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
Only heard the RME which I have and it’s very very good. The awesome EQ and features I believe makes it a big extra advantage over the others. 
One of the few pieces I’ve bought new over the years and felt I got more than I paid for. 
The black ice dac above is a really great smooth dynamic unit. Not sure about mqa or quality of its headphone amp. Actually thinking about picking another one up as a 2nd dac. 
i have my fx tube dac still... after reading the stuff about the shootout in arizona -- bought it stock sounded very musical but somewhat rolled off and veiled with good tubes in it (stock chinese tubes turn up the treble some, but a little grainy) then sent to chris j/wally to upgrade level 2 mod - comes back cleaner more transparent more extended - sounds right with proper, good old stock ax7’s in it but the treble can still be a lil problematic (sibilant) now that caps and wiring have delivered excellent extension - maybe the thing needs a thousand hours of break in lol...

sibilance not as bad as dena ares2 or bifrost mb, but still there on some material - tried various cabling...

so overall i like the mhdt and audio mirror (with tube upgrades) more, or the lovely older mf trivista or ava fet topp dacs more than the fx for ease musicality and insight without force feeding treble detail -- but i haven’t thrown in the towel yet on the fx

i am not a headphone guy so can’t comment on how good the hp output is... but that lil volume control is not the greatest... imo best to leave it on full blast for most clarity and control volume elsewhere