the cart or the horse?

I would like this amp to be:

modest in size as to more easily pass the wife test
have a remote
no phono pre amp is necessary
no preference as to tubes or not as I have never heard a tube amp
used because I may not like it and will want to recoup most of my money through a resale

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.