Integrated Amps

I am quite impressed with the Soulnote A2.  I see it occasionally only used for under 5k.  It is SS but has a wonderful warm but resolving sound.  From your list, and other recommendations, I can only say it is much nicer than the PS Strata, or NAD, which I have owned or heard.  Very high quality build, and completely transformed a second system.  I combine this with an Auralic Altair G1.1, a value oriented piece, and it sounds very good.  There are many fine integrateds for sure.  Keeping the DAC separate is very flexible going forward.  The Soulnote developer left Marantz to create better sounding components, and not have his hands tied by corporate ownership.

If you are thinking of upgrading your speakers the advice of upgrading those first, prior to the integrated is really good advice.  Synergy as noted in several responses is so important between gear, especially speakers and amp.  It’s tempting if you are going with an Integrated to get an Integrated with everything, DAC, Phono Stage, Headphone Amp, the list goes on.  Really good advice I got from others is to focus on what sounds best in an integrated, getting the best pre / amp combo.  The Phono Stage, DAC are items you can add into the mix and you’re likely to get better performance and flexibility by going that route.  If you have your heart set on an Integrated, one box that has everything and does it all well, the NAD mentioned in this thread is an unbelievable value, great performer.  The streamer / DAC built in is extremely well done, has room correction, really does it all and is about as future proof as you could hope for.  
 

Integrated Amps I’d add to your list: 

Parasound HINT 6 - incredible value, bang for the buck, SS and can drive almost any speaker

Coda CSiB - Coda is probably the most underrated high end Hifi manufacture out there.  The engineering, parts used and overall build quality are second to none, it’s not cheap but you’ll pay many multiples above there gear just to match it, it’s a no frills integrated, can drive pretty much any speaker. 

Krell 300i - might be the most magical Integrated I have heard, something about the combo of power, control but also a liquidity, tubelike quality without any of the draw backs of tubes.  

PrimaLuna Evo400 - All Tube Integrated built like a tank, no frills. 

Linear Tube Audio - several Integrated Amps - like Coda, incredible build quality for the price with top notch engineering, if you want Tubes, really hard to beat and incredible value relative but not cheap. 

McIntosh is a polarizing brand but they make solid state, hybrid and Tube Integrated Amps, hold their value like no other brand. 
 

Hifi Rose RA180 integrated - highly reviewed, very well done Class AD amp, will drive almost any speaker

Niam - make several integrated amps that would cover all your bases, well thought out DAC/Streamer built in

Hegel - 3 different models, often one of the most highly recommended by those who own one.  Very well done streamer/DAC combos, if you add a separate streamer / DAC can raise the performance which is already really, really good.

I’d buy used, buying Hifi gear is like buying a car, it depreciates 30-60 % as soon as you open the box, you can really stretch your dollar going used.  Good Luck

Pass Labs INT-60

Class A to 30 Watts

The Audio Research i50 is a fantastic integrated. They have a DAC and Phono stage card upgrade as well. You can find them on HiFiShark for under 4K.  That's a LOT of amp for not much money.  I think they sound fantastic- typical ARC sound- tube warmth with analytical precision, 

https://www.hifishark.com/search?q=audio+research+i+50

Marantz makes some pretty good integrateds, better than many of the non-japanese designs simply due to Marantz (like Yamaha, Sony, Luxman and Denon) knowing how to design a quiet circuit. I haven’t heard the Billie. It gets good reviews but I’ve seen quite a few of the mkII version on the pre-owned market already—unusual for what I imagine is a low-volume product. 
 

For integrateds, I haven’t encountered any that outperform the Yamaha A-S2200 or A-S2100 for their street price. They combine the good traits of tubes and solid state better than any of the hybrid tube/SS products I’ve used/owned. Usually with the latter, instead of the “best of both worlds,” you instead get the worst of both.