the cart or the horse?

@wavendon

Without question you’re going to receive a multitude of different suggestions, so I may as well offer mine. IMO the best part of your audio system are the Omega speakers, I’d keep them. I believe that you’ll get much more involving and emotionally engaging jazz playback with a tube amplifier.

Fortunately you don’t need high power and I disagree with the the comment above with regard to low power amplification. The Omegas allow you to to focus exclusively on the quality of the amplifier rather than getting more watts.

For example (And there’re numerous good ones)

Luxman SQ -n 150

Coincident Dynamo el 34SEP/300b SET

Dennis Had Fire bottle SEP

Decware SEP several model choices.

Anyone of these choices would sound "much" better and involving than your current amplifier/preamplifier chain. Your jazz recordings will spring to life and pull you in deeper to the music. Your Omegas are not the problem. After improving the amplification I would next upgrade to a higher quality seperate DAC connected to your current music server.

Charles

I agree with @charles1dad. The Omegas are the jewel in your system.  Tubes or perhaps SS class A would probably work great. 
 

   I used the internal DAC on the Bluesound for a while. It was adequate,but a decent external DAC will most definitely be a large improvement. 
   Enjoy the journey. 

Loudspeakers first perhaps Triangle Esprit Titus EZ. Next would be your amp, we can talk about that once you change your loudspeakers. 

The Omega 7's are the hidden jewels of the Omega line.  Go for a quality hybrid tube integrated ... Rogue Sphinx 3 (new @$1600) ... and you should be in business.

Stereophile review - Rogue Sphinx

Sphinx Info Sheet

Rich 

I would like to agree with the excellent advice on upgrading your preamp / amp to as good a quality tube equipment as you can afford. I would invest in that first. Then, enjoy, save up and work on a good DAC… then upgrade your streamer. Then you can work on interconnects and cables.

Keep with the long game, 0ne step at a time. Luxman would be a good choice. An integrated tube preamp/amp… spend your whole budget… then save up for your next step.

Also, speaker positioning  can make a huge difference if you have latitude to move stuff.