Floorstanding towers

I second the Vandersteen recommendation.  Would also suggest Magnepan (Several new or used models in your price range), or a used pair of Quad ESLs, either the 57 or 63 (and its later derivatives).  Dipoles do really nice things vis-a-vis room interaction.  I  like some aspects of the Martin Logan presentation a lot, too, but you'll have to listen and see if you hear the transition between panel and woofer ... I suspect ML has gotten better at this since I last heard them in the late 1990s.

The Tektons are potentially interesting too - big, efficient speakers do things nothing else does in terms of dynamics, scaling, and lifelikeness.  It might be worth emailing Tekton to see if there's somebody in your area who'll give you a home audition.

I'm a shill for Salk speakers having owned 6 pairs. For the money - can't be beat.

I also third the Vandersteen recommendation. The higher end models are sublime.

You would do yourself a disservice to not check out the Double Impacts.  You will not get a beautiful cabinet.  You will get the best sound for you money.  The value on these is off the chart as is the sound quality.
I've learned to really like the satin black cabinet that does not call attention to itself.  Fades into the background and all I hear is a huge detailed airy soundstage. Beautiful.

Having just put a system together for my girlfriend after a hell of a lot of research, and looking at many tower speakers right in your price range (her preferred style over mini monitors and size considering her room etc..). I unfortunately couldn’t audition everything, but after weighing many reviews and subjective user comments, I landed on a pair of PSB Ts.
I am thoroughly impressed with them. Very well balance, produces enough well defined bass, a beautiful luscious mid-range, on through to and very refined high top end with their titanium tweeter. A very well balanced speaker. I really can’t complain about anything... And they look absolutely wonderful with a build quality beyond their price point. The dark cherry is gorgeous. These should definitely be on your short list for consideration.. I know the competition is stiff in this category, but these are something.
FYI, I mated them to a Peachtree Nova150, Cambridge CXC CD transport, Rega P2 with AudioQuest cabling. It all matched up well and is one hell of a sounding system for the $4500-5000 range. Punches way beyond it..

You could narrow things down quite a bit by defining your "flavor" preference. For example, I have am a detail/clarity/sparkle fan who loves female vocals. I like a speaker that some others would consider bright; but actually measures very linear. I have Canton 3-way bass reflex towers and Boston Acoustic 3-way acoustic suspension mini towers. 
While shopping for the Cantons last year I auditioned in reverse order of preference Golden Ear Triton 7s, SVS Ultra, Elac not sure of the model, I think it was an older European one, and SVS Prime. The Prime was very nice to my ears. Of course, many people love a rounder, softer sound signature without sharp edges. And the U shaped response curve is still very popular. What's your favorite flavor?

The closest Canton model currently available to the used ones I bought is the Ergo 690. They can be had new for $2,800 a pair.
https://soundapproach.com/canton-ergo-690-dc-tower-speaker-single.html

If I hadn't found such a good deal on the Cantons; I was very interested in Tekton.