Allow myself to introduce...myself

Welcome to this interesting and informative site! Regarding upgrades I recommend replacing the Adire's with a used pair of DCM Time Windows. They offer a significant improvement over your present speakers and can be bought cheaply! I paid $219 + shipping for mine (the third pair I've owned!).

Welcome! coldducktime
there has never been a better time to get into this wonderful hobby.
Much gear is avail on the used/demo market. Watch this site, as well as, eBay and US Audio Mart every week. If you are fortunate enough to have local dealer/retailers, visit regularly and listen to as much gear as possible.
Have fun.
Happy Listening!

Thanks for the suggestions everyone. 

Regarding my generous budget, it is somewhere in the many tens of dollars. My first career as a woodworker left me broke and I couldn't afford to improve my rig. Now I've changed careers, but with my background a good set of DIY speakers would be a breeze for me. 

My first step might be to get the Sumiko BPS retipped, at some point a small child or cat broke it, I've been limping along with a red Ortofon. The GAS Thalia has gotten a bit noisy in one channel, even after cleaning all the pots and contacts. I'm sure it's repairable but I wouldn't mind something new. 

I don't know where all the used hi-fi shops went, I would love to spend a day auditioning some gear. I live in the SF East Bay so if anybody knows any secret hole-in-the-wall shops please let me know.

Check out my rig in Virtual Systems. Click on my name and click Details to get an idea of the more frugal route to great sound. 

^^^  noromance ...

Love that vintage system. If I were starting over, I'd go for one of the rebuilt classic turntables with the custom plinth. I have a couple of friends who have done so ... and those tables interject life into the music that has to be heard to be believed. 

Frank

Thanks @oregonpapa
The thing is it does NOT sound mellow, laid back and "tubey". It’s pinpoint, neutral, and crystal clear with good resolution and unbelievable bass (for Quad 57s)

There are many ways to "upgrade".

What are your specific goals?  

Your SOTA is still just that with some TLC
they still make and service that model for a reason.... change that last
and pay it forward by giving it away ( just like how you arrived at it )
speaker cabinets are more than fine woodworking but have at the DIY sites or maybe re veneer any number of great and affordable speakers - for example the DCM Time windows might look smashing in an all wood cabinet, ditto Vandersteen 2, Thiel came with nice cabinets as did Snell, Dunlavey
maybe rebuild and upgrade some Dalquist, etc

Hi,
Welcome.  Cold Duck Time is one of my all-time favorite jazz recordings by Eddie Harris.  You have a nice audio rig, for sure.  I just parted with my SOTA TT after 32 years to an analogue lover.  

My best modestly-price suggestion is to upgrade your your speaker cable to Dueland 16 ga. wire with the terminations of your choice.  Shunyata Venom IC's are about $100 a pair and really elevated the sound quality of my system.  Good upgraded cabling is the least expensive way to improve the sound of your system.  

noromance I love those Garrards with the fancy plinths, never thought of doing that.

The SOTA isn’t going anywhere, I’ve always been very happy with it. Good to know I can still get belts for it. The suspension does sag a bit on one side but I level it to the platter and everything is groovy.

I am fairly happy with my Adire DIY speakers, they do a decent job with imaging but where they really shine is the bass, it is the most warm, controlled and lifelike I’ve ever heard outside a jazz club. And they roll off quite deep in the range.

The rich guy who gave me the SOTA played Bru’s "Time In" on his Vandersteens when I picked it up. The opening of "Lost Waltz" was an experience I’ll never forget, when the band explodes into that scorching romp. It was like being in the studio and the hair on my neck stood up. The Sumiko BPS definitely had something to do with it. So that is something I am interested in recreating, my current setup doesn’t quite get me there.

Whitestix, yeah that Swiss Movement album is an absolute blast. The energy between Les and Eddie goes straight to your soul, and it's so fun to hear the audience's reaction.

I spent a few years as an A/V technician, and understanding what I do about electricity I’ve always had a hard time believing that a cable could have much audible effect, at least to human ears. But, heck, maybe there is something to it.

I do also believe that the most important place to spend money in a system is anywhere that energy changes state, such as a stylus or speaker. These devices require the highest level of engineering and materials to minimize distortion.

I use $30 power cord from BLE Design on eBay. Definite improvement in SQ. Tightening up of focus and blacker blacks. They use OFC wire and fancy sheath and hardware with a choice of plating. Well worth it.