A rookie with 10K, seeking advise

Throwing out small suggestion on how I would spend your money😁 Luxman 505UXii. Spendor A4 speakers easy to power and room friendly. You can add a Bluesound node and a RME-ADI dac. That would be close to your 10K budget.

your speakers and amp are just fine. What is your source?

You speakers are what talks to your ears.  Without quality speakers you may not be able to hear the benefits of upgrades.I say spend $6,000 on speakers...sell your lintons and Strata and that $3000 gives you 7,000 to spend on amp, music server, power cords and interconnects. $5000 on a luxman or Accuphase...2000 on a music serve...

Upgrade only one item at a time or you won't know the actual impact of the individual items. Speakers generally have the biggest impact and are the easiest to hear a change in the sound quality and should be upgraded first. There are a ton of great speakers out there to choose from between $5 and $10K. 

After that and only after that should you consider upgrading your integrated amp if so desired. Allow the speakers to break in per the required time and then see how your current amp and speakers actually perform together as a system.

Your PS Audio Strata Integrated is a very decent amp at that price level and the rule of thump is you have to spend 2x the list price amount to get a noticeable difference but different amps could also have different sound characteristics so that would also come into play in spite of price. 

Coming in late to this discussion, but it reminded me of where I started a few years back. I would make two purchases:

1. Harbeth 30.2 XD speakers 

2. Dynavector XX2 Mk2 cartridge 

From there you can eventually upgrade your amplification, phono stage and turntable/tonearm. I would also suggest a call to Gene Rubin, who is a master at this kind of plan!