the cart or the horse?

Doesn't meet your remote speck but it would sure leave you with enough money to purchase a preamp like the Schitt Saga + to add the remote.

The Musical Paradise MP-301 MK3 Mini Tube Amplifier with Headphone Output 6.5 watts per channel.  allows you to change tubes to fine tune the sound profile for very little money.

Better than used and if you find you don't like it pretty easy to get most of your investment back.

Hello,

The week link is your preamp. If you want separates start with the preamp like a Rogue RP-1. I would keep it simple since the amp is just ok. Rogue Sphinx v3. If you don’t care about the phono preamp get a used V2 and then work on a great DAC. 
Just so you know the BlueSound is a great app. Sometimes when you go to a new DAC and streamer you lose that great app. 
How about a simple NAD 316 Bee. With your BlueSound Node 2i this will do great. Then save up for a killer DAC. 

Should I consider something like this

https://skyfiaudio.com/products/sansui-au-6600-integrated-amplifier-super-clean-from-the-70s

@wavendon

I would not. For your Omegas, the suggestion from @danager ,the Music Paradise MP-301 is a better option.

I say this based on your expressed desire for sonic "body and presence". This is an inexpensive integrated tube amplifier that has a consistent word of mouth reputation for good sound quality.

This very simple circuit tube amplifier will pair beautifully (IMHO) with your very simple single driver speaker. I believe the body, presence, tone/timbre and 3-dimensional space will be much improved to what you currently have. All this for less than 500.00 USD. Earlier in this thread I listed some recommendations for you.

All excellent choices for your objectives but more expensive  (But worth it). So if you’re leery of spending money then this MP-301 is a very good option to consider. Your jazz will definitely sound better than what you have now.

Charles

If it were me (it’s not) and I already owned those Omega speakers, I would be looking at one, or more, of these integrated amps to replace your existing pre-amp and amp:

Musical Paradise MP-301 MK3 Mini Tube Amplifier

Rega Brio (current model, not the Brio-R or original Brio) or Rega io for less $.

Dayens Menuetto Integrated Amplifier

They are all WAY below your max budget. Heck, I might even buy a couple of different ones, do a shootout, then return (if they have a trail period/policy) or re-sell the loser.

The Rega is probably the most popular, but it’s also the most expensive. I own a Rega Elicit-R and I love the Rega house sound. However, I might be tempted to try the other 2 based on their prices.

@reubent

Good posts. @wavendon has gotten numerous worthy suggestions on this thread. I don’t have a good feel or sense as to how committed he may be to getting maximum sound quality his budget would allow. Earlier atmasphere mentioned the Leben 300 integrated tube push pull amplifier which uses the el 84 output tubes.

A bit over the stated budget but an excellent recommendation. I had previously recommended the Luxman SQ N150 which is also another high quality el 84 push pull Japanese tube integrated amplifier. Similar to the Leben but a little less expensive. Either would allow the Omegas to sing at a very high level.

I mentioned the Coincident Dynamo MK III which is a bit different. SEP class A with a triode wired el 34 with zero NFB circuit. Priced under 2,000.00. All three amplifiers are from highly regarded manufacturers and will employ very high quality parts, output transformers and power supplies. This is what the higher cost gets you. I’d shoot for the quality proposition.

If the OP really wants to go for it with his very fine Omegas then these higher caliber tube integrated amplifiers are the way to get there. All of the body, presence instrumental tone (Acoustic dominant jazz instruments) dynamics and transparency one could want at or near his stated budget. That 15’x10’ room would transform into a really nice jazz venue like environment. It would sound gorgeous.

Charles