Full Range under $5k-ish

I used to use the TFM-35’s many years ago. I Don’t know if they were the x’s or not.  I then purchased a demo pair of Thiel CS2.3’s and connected it to the Carver.  The sound was so shrill, that my wife refused to let my play any Music. She thought the music sounded like fingernails scratching a chalk board. I replaced the Carver, with a Plinius 8150 and my wife let me listen to music again.  My wife and I I still enjoy the Plinius/Thiel combination that is decades old and now located at my mountain home.

The Carver worked very well for many years in my home theater system with real M&K speakers.  IMO this amp is better suited for home theater than music.

Based upon this experience,  I am in agreement with cedargrover that you make certain to test potential speakers with at least one of your Carver amps prior to any final  purchase.

Op if you can go up a tad to $7k you can look at a set of Legacy Audio Signatures. 

These should be perfect for you:

1: They are 93db efficient so they will play loud with any amplifier
2: They have bass down to 22hz
3: They throw a huge soundstage
4: They have high power handling. 
5:  They are easy to drive  
6:  They have superb  top end detail

If you want to fill up  a large room these can't be beat

Dave and Troy
Audio Doctor NJ Legacy Audio dealers

A plethora of recommendations, as usual! Let me add another: ATC SCM 40. Should be around 4k; if not, go for a recent pair of used 40 or 50 in your price range. Stunning dynamics, imaging, and detail (not harsh). Need power, but you already have that.

You can get Focals for your price range.  Not their top of the line stuff, which is out of reach for most people.  ATC seems to be with-in your budget.  If I was spending 5k on speakers I would audition them at home.  Golden Ear is a close match to your Def Tech's in sound.