Full Range under $5k-ish

Be brave and get a pair of the D&S Tech Labs FM2's, around $5,000.00 and they will satisfy you for years until you upgrade to the FM4's.If you are in the Chicago area you can come over and listen for yourself.Great speakers that no one has heard of, and no they are not HT only speakers, the bass is awesome and can handle whatever power amp you can throw at them.

https://libertyaudio.com/service/x-vox-loudspeaker-system/

From its maker

Good Listening

Peter

Have a look at Zu speakers.
They sell used (trade-ins)as well as new and have what they call a "dirty weekend" deal where you get some sent to you and send them back if not suitable.
All their models are high efficiency.

I have a pair of Soul Superflys and love them.

I would audition/think about MartinLogan ESL X or ESL 9 or
Magnapan 1.7 + a subwoofer for example MartinLogan 1000W or REL T/9i, (maybe that is cheating/not full range but that would be rather high budget)
In case you prefer planar Electrostatic or Magnetic like I do.

Assuming New?

I’ve been through a number of speakers the past few years. I’m a classic rock fan, I listen a bit loud also. But at your price point, for new speakers it’s pretty easy for me to narrow it down to 2 speakers. (if you can ever so slightly bump your budget a bit)

Ohm Walsh 5000’s (essentially have a 4 band EQ on the back) can be placed close to the wall. They love power (which you have) plenty of bass (even for me). 6500 new, the 4900’s are a massive bargain with a bit different form factor. I have the 5000’s and love them. First speaker that I absolutely love in a long time. Added bonus - your kids can not hurt them (if you have prying fingers etc). John at Ohm a good dude to boot.

Salk Song 3 Encore - will play deep, with a nice amount of bass. INCREDIBLE craftsmanship, a bit more detail than the Walsh, not quite a big of a soundstage. (I’ve demo’d them several times, very good speaker, I owned the SS8’s) Plus Jim at Salk is a good dude also. Will play deep, have some thump but won’t move as much air as the Walsh speakers (the Walshes can absolutely thump a room if you want them to)

I love the OHM Walshes, you did mention you like Focal and Wilson (both with the focal tweeter I'm wondering?)

The Salk might get you closer to that sound.  Probably a bit more detailed speaker.

The golden ears, honestly are nice but not THAT much different than your DEF Techs. (I’ve owned the Triton 2’s in the past)

I also like the Vandersteen sound. That said, I think the OHM’s give more bang for the buck. I like that big, open natural sound. The Quattro CT’s I love, but well... they are 14k a pair.

Personally, try as I might, using EQ and everything else I can never get a sub to totally integrate with my mains. I like a very coherent sound and a big open sound. The OHM’s give that to me.

ATC’s, also nice very detailed yet uncolored midrange. A shade bright to me and you have to spend a LOT to really get that thump. But very nice stuff.

USED - well that opens up a host of options.