What to upgrade next?

Of the three choices you listed to me absolutely power tubes. You can do much better than JJ and the change in sound quality is  dramatic and substantial with better tubes. That being said ohhwy61 has some good thoughts above on positioning which is indeed free!

Yes we are in the process of changing our generic entertainment center to a custom walnut slab unit. Not necessarily specifically made for audio but it is very solid and wifey approved. The TT came with 3 point isolation pointed feet so hopefully that is correct isolation. I thought about the Zu version of that cartridge but they were out of stock a while back when I was looking into it. I've since come across SoundSmith and was wondering how much improvement that brand might bring in. I can move the speakers around a little bit but the location in our room is a bit limited. 

Rick

A vote for power cables.

I've gone through all kinds of upgrades--though always in a solid state mode. in upgrading components, clearly the biggest improvement was going from 80 watts to 200 watts, and again to 500 watt mono blocks. bigger impact that speakers, cd players, network streamers

in accessories, and i am still surprised at this, biggest improvement cape from power cables, better than speaker cables, ICs, digital cables, brass footers, maple plinths. The brass footers also made a big change, but only on my Cyrus cd changer, not on other components or my Marantz SA8004.

All of the upgrades improved things to various degrees, but the amps and the power cables were the biggest change.

Power cables made a big difference in my system too. But I also use 500wpc amps, so the 14awg cords that came with them, while acceptable, were definitely restricting the sound. I’m not sure if my experience with class d monoblocks will translate to your <10wpc tube amp.

Might I recommend vibration control as well? For the TT and integrated tube amp, spring suspended platforms will open up the sound and reduce the noise floor. I made my own from wooden platforms I cut to size and placed on top of properly spec’d springs. But there are plenty of commercial options as well.

Falling under vibration management, tube dampers can help improve your sound as well. I have a tube preamp that has a noisy power tube. Tube dampers dropped the noise coming from the tube noticeably and improved the sound of my system, so I decided to put some on all my signal tubes as well. That made a slight improvement, but not as noticeable as damping the noisy tube. But they’re very inexpensive, so it didn’t hurt to try.

With regards to tubes, I replaced all my stock Chinese tubes with better (but not TOTL by any means) modern Russian tungsols. In doing so, I noticed more of an improvement when I replaced signal tubes than power tubes.. but your integrated doesn’t have signal tubes, and I did notice an improvement with better power tubes, so that could be a good route.

Again, based on my experience with a decidedly different system, isolation platforms and cables made a bigger difference than tubes, unless your tubes are quite crappy.. I’ve had no experience with JJs, so I can offer no advice there.

Good luck!

I would get better tubes.  Most manufacturers include the JJ tubes because they are inexpensive.