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
Nuprime makes some good gear too, though I think they have just introduced new models...I think some of the confusion mentioned before is that while the title states w/built in headphone amp, the OP also states he is considering a Schiit DAC with separate headphone amp...
Lots of choices here of DACs, so here’s mine. I have Benchmark DAC1 that I have had for many years. It sounds great and can be used as a preamp. The Benchmark DAC1 MSRP was $995, but can now be found for $500 or less. With your budget, you could probably find a DAC2 or a DAC3 that would meet your needs. If you are looking for a smooth sound, I recommend a tube unit. In any case, I think it makes sense to listen to as many as you can before you decide.
The Wadia Di322 is out there in the wild if your patient. Its a good DAC and has headphone capability;  2 coax, 2 optical, 1 USB inputs plus XLR. Does DSD. ESS Saber 9016S implementation. Very similar to the Mcintosh D100 I believe.

Might find one in your price range.
Caveat: Mcintosh group has shelved the Wadia line but support service is available.
The newest Cambridge Dacmagic looks pretty cool...MQA and all. I have an older one and it's great sounding. I also use a Schiit Bifrost 2 with a "Bluenode" 2i for MQA streaming although I rarely use it with headphones. Headphones in bed reading, pair of awesome Grado 325e with a Schiit Magni 3 from an old iPhone...yeah man... 
My 2 cents - used Chord Hugo 1, used/new Okto dac8 Stereo, or new Audioquest Dragonfly Cobalt.