Integrated Amps

I’ll offer my two cents on the Billie amp. I had the Mark II version for a couple of weeks to try it out. I was very impressed with the build quality, the design and the functionality of the user interface. I can’t comment on the built-in DAC or the Bluetooth as I did not use either of those functions. 
The sound quality I thought was very muscular with a clean mid range and good high-end extension. The bass was strong, but clean and very well-controlled. Overall, I was very impressed. However it wasn’t a good match with my high-efficiency speakers. I imagine that it would be a very good match for speakers that require a lot of drive such as panel speakers or those which with large heavy drivers that need a lot of control. 
The manufacturer took the return with no hassles and they were very easy to work with. I believe there’s a 30 or 60 day return. So it might be worth a shot.

@bipod72  as ​​​@ghdprentice noted, whilst appreciating your primary interest in the Billie, looking at the costs of others you noted such as the PS Audio one for potential consideration might be the NAD C399. It has a just about everything uprated from the C3050. Which was why I bought one for my Daughter and Son-in-law for a Wedding gift and seems to tick a lot of your boxes, apart from the tube point of the billie, but perhaps a tube stage later if you use/go MC could give options.

It has 180W/ch continuous (250 peak) hypex so power wise your speaker upgrade is well catered for and the Hypex modules stand up relatively well in my Trinnov Amps for musicality when I have tried them against my Vitus SS103.  The NAD built in phono stage has had some highly complementary reviews as noted at https://www.theabsolutesound.com/articles/nad-c399-hybrid-digital-dac-amplifier/ stating quietest phono stages he had heard below a $29k separate and better than he had heard integrated outside his Mcintosh C53. But an AV forums review was a bit less enthusiastic on the stage, but didn't give the amp less than 9/10 in any category.

As it was 'boxed for present' and they live a 100 miles away I haven't listened to it alongside my Whest MC Ref's or Titan Pro II. But on their system Project X2, with both an Ortofon 2M blue and even more with an LVB 2M black it sounded very good, both with and without the option of built in Dirac, which is another bonus if you would consider / want room correction, there are two MDC module slots with the BLUOS-D that has the Dirac taking it from quoted $1999 for the amp with MM etc to $2598 with the module, but it can be added later.

If you are MC on the phono the review above was complementary of it with a quicksilver SUT. Personally I have not been able to find an SUT+MM into any of my pre's that get near a Whest 30 SE or above.  If you are or might go MC there are guys on here who could recommend SUT's.  But if vinyl is your prime source and you are/ will be going MC I personally would be considering MC Stages with a Whest on the audition list as I have put mine through a 25 year old Sony integrated that was designed for SACD and notwithstanding limited power the capability of that as a source shone through, but that is if you were considering a different path and others mileage will no doubt differ and as noted, you could go tube phono.  

The C399 has a built in headphone amp which I note you wanted. And my son-in-law reports the Apt-X Bluetooth (which I believe is 2 way) is certainly the best source he has heard into bluetooth headphones when he is outside.

So MM whilst stage could be the limiting factor, it is with a lot of integrated amps. But seems to meet enough of your requirements that a listen could be worthwhile.

Class D look for the gato dia 400s and a very good dac.

I went from Marantz to Musical Fidelity m6si and have been happy.   Gave me more power and a familiar but better sound.  I took my speakers to a few whops and listened to several to make sure they matched up.  If new speakers are on the horizon, agree with others to match them.  

Also, I use my old Marantz, repaired, to drive outdoor speakers.  Might work for headphones too depending on your situation. 

I resurrected my system five years ago by purchasing a Yamaha A-S3000 integrated amp. It was a huge sonic improvement over the Yamaha A-1000 integrated I bought in 1985. It was easy to discern because I had the same speakers, Infinity RS-4b’s.

The sonic improvement was the start of a very deep rabbit hole for me. I upgraded speakers next with Magico A3’s. Then I listened to a Prima Luna integrated amp a buddy let me use. That led to buying a Dynaco PAS-3X tube preamplifier. I paired that with the A-S3000. The sonics were an improvement over the A-S3000 alone!

I’ve since upgraded the preamplifier, the power amplifiers twice with two pairs of mono blocks, added a separate phono preamplifier, upgraded the turntable, cartridge, cables, power cords and added room treatments, Soon the power conditioner will be next.

I’ve enjoyed the journey but I was naive as to what I was getting into when I upgraded to the A3’s in regards to what it would take to bring the sonic level of my rig up to what I heard in the demo. My advice is to proceed cautiously.

Obtaining synergy between components most likely will become very expensive. I also have another rig which uses the old RS-4b’s with a Scott A 436 integrated amp and McIntosh MR-55A tuner. I enjoy that system almost as much as the main rig when I listen to it!