What I see, listener fatigue at volume, but not sure which component(s) are to blame. Odds are Klipsch, they play loud but not smooth and stress free. If you can sell those for $1k (or more?) then your $2-3k will get you comfortably into Tekton Double Impacts https://www.tektondesign.com/double-impact.html Don’t worry about not being able to audition. I got Moabs last summer, Eric Alexander makes some absolutely fantastic speakers. Clean, clear, dynamic, extended, neutral and most importantly in your case absolutely strain free. If you experience any fatigue whatsoever its not from the speakers!
Strain and listener fatigue can also come from electronics. I’m not gonna mess with your digital, it is after all just digital, it is what it is. Not gonna touch your table either, already said not a lot of vinyl. Plus doing that before the rest of your system is prepared for quality vinyl playback is kind of a waste.
That leaves your amp. Carver and tubes are okay but I will say sell them both, along with the interconnect and whatever power cord they are sucking up, and get one of these: https://www.ravenaudio.com/product/nighthawk-mk3-tube-amplifier/ Yes that is plenty of power. If it doesn’t sound more powerful, with better bass and everything than your Carver, I will eat this post. Which would be quite a stunt if you could see it, only you won’t, because when you hear it you will agree.
I am still leaning Double Impacts, offering this more to give you some idea where you could be going. DI/Nighthawk would be awesome and crazy good for the money.
Last idea which depending on how you do it, could be done together not either/or- springs or Pods. Springs under your speakers (and everything else) is a huge upgrade. Nobsound springs from Amazon are terrific high value and very versatile. There’s also plain springs but they are a lot of time and trouble to figure out. Finally there’s Townshend Pods, by far the best but also most expensive.
Springs made a huge improvement in my system, particularly in the same area of shouty fatigue, taking the sound in a much more natural smooth direction yet doing this without losing any detail. There is in fact more detail revealed now that the ringing is gone. https://forum.audiogon.com/users/millercarbon
I got this with all 3 types of springs, they are all in there, which is how I know they all work, and which works best, and for what value. Townshend cost more but are worth it, they are just as good value as the cheaper stuff. http://www.townshendaudio.com/hi-fi-home-cinema-equipment-vibration-isolation/seismic-isolation-pods...
(Search eBay for plain springs.)
Same for the others. Speakers or amp. Its all down to how you want to do it, and in what order, etc. Any one of these will take you in the direction you want to go- and you will be surprised how much.