WILL IT MAKE A DIFFERENCE?

The room sounds like it’s bright to me. A good tube amp will not differ much from the Hegel. A bigger and/or a newer one might help you.

Or go all in with Atmosphere.

For me, the biggest difference going from a SS to Tubes is your ability to create your own sound through tube swapping.  I started with a Raven Reflection MK2 integrated amp that drove Wilson and then Sonus Faber speakers.  I then went with monoblock tube amps.  The sound is just lush and very musical with tube amps.  I like your thought on Joseph audio speakers.  This is a hobby that we tend to buy and sell equipment searching for that elusive end game sound which we will never find...lol.  There are so many options in the $7-10k price range.  I am to the point where I have end game Amps, DAC, Speakers and Music Server.  Now I am testing different Power Cables, RCA and SPDIF cables.  You did not mention what cables you have but they can make a big difference in SQ.  

My experience over the last fifty years has been a slow nearly inpercetible move towards tubes. First to an Audio Research tube preamp, then an Audio Research tubed phono stage, then ARC tubed amp… and finally an ARC tubed DAC.

Each step added musicality and better midrange bloom, lower noise floor, and absolutely no fatigue.

Of all the integrated amps I have heard, I like the ARC VSI 75 the most. To me it really captures the essence of what is beautiful about tubes. incredible mid range, well articulated bass. Would be a huge upgrade to your system.

I would recommend finding a dealer and listening to it. Worth a trip to a nearby city if one is not near.

You could look to swap to warm interconnects and cables… but give you have an opportunity for such a large upgrade… well you can’t do that with cables. Also, it sets the stage for future sound quality improvements to source components. There is a big difference between a $4K integrated amp and a $10K integrated amp. You should be able to trade in the Hegel.

Wives will frequently say they like the sound to discourage additional audio purchases. Females have much more sensitive hearing… if I thought my system was fatiguing (and I can’t tell you how intolerable that is to me) then your wife should be screaming in pain. My partner finally absolutely loved my system only when it became an all tube system. I would bring her along on auditions for her to inform me of high frequncy hash and distortion, just out of my hearing range that I would discover later.

My wife, a professional orchestra and chamber music player and singer much prefers tubes. Me too!

In my experience, the best way to tackle listener fatigue is to treat your listening room with a combination of absorption and diffusion panels. If done properly, you should never have to worry about brightness and/or listener fatigue again. I use GIK Acoustics.