If you are ok used, find a pair of Dynaudio Contour 1.8s. They’ll be well under budget. I’ve used the 1.1’s for years with my Willsenton R8 which shares some similarities with the Evo 300 and the sound is thick, warm and punchy. The 1.8’s are in my HT system and go even deeper and are a bit more efficient. I use KT88s though. I’m not sure if the 120’s trade some midrange for sparkle/bass, so maybe also a set of KT88s or even el34s if you still have the original tubes.

https://www.sonusfaber.com/en/products/sonetto-iii/

Check out Totem. Most have a small footprint and sound fantastic. 

I would highly recommend considering Sonus faber Sonetto - I heard them with Rogue integrated and was blown away by them

 Check out Salk Sound.

Monitor Audio

There is a pair of Spendor D7.2 floor standers listed here for $5500. Make an offer on them! I doubt you would go wrong with a Spendor!

Wharfdale Lintons. Stereophile class B. Add a subwoofer and they can jam better than most bookshelf speakers and better than a lot of tower loudspeakers. Very close to the Grado sound you are looking for. Tubes or solid state will work fine. A pretty good deal on top of that. Good bang for the buck. 

I have owned Salk Beats for almost four years and love them.

If the Sonus Faber Sonetto III are of interest, contact me. I have a pair in wenge available.

I posted this earlier that got removed and I can’t begin to understand why as it violates none of their guidelines.  Oh well, here goes again…DeVore would be good speakers to explore as they’re natural and slightly warm sounding and are easy to drive for tubes.  The Gibbon range is slim, and here’s an example of something you might like to consider.  Best of luck. 
https://www.usaudiomart.com/details/649970845-devore-fidelity-the-nines-great-condition-walnut/

I would stay away from the Lintons, for my bad personal experience and advice from Upscaleadio

Maybe I dont get your tastes (thick and real?). I like transparent and detailed (natural sounding). I would audition (in your price range): Martin Logan ESL X, Tannoy Eaton, maybe some Magnapans or KEFs or Lii Songs. I tend to always enjoy electrostatics and concentric dynamic more than other designs. I have older Martin Logan Source connected to my (older) Prima Luna Prologue amp and really like them. I also have your Grado headphones, but rarely listen to headphones, and prefer my (more expensive) HiFiman HE6 planar-magnetic phones anyway.

Audio Solutions FIGARO L. I have a pair of FIGARO and they sound fantastic with most genres of music

Omega Speaker Systems

Super Alnico High Output XRS

Proac D30RS would be glorious! The voicing of the speakers are mid-range focussed, with sweet highs from ribbon tweeters. The bass, though sufficient, can be supplemented by Rel subwoofers (if possible). If you like lots of bass, you can try D48 speakers, whose sound is big, and all encompassing. I have had both and I miss my D30RS 😢. 

Monitor Audio Silver 500 7G. Stereophile Class A rated - and if you listen to them you'll understand why. The combination of effortless clarity, dynamics, range and soundstage are hard to find in a single speaker, let alone one that costs only $3400 per pair. With you Evo 300 you have 100+ w/Ch, which means a pair can generate roughly 113 dB in a typical listening room. That's really loud, so you're Led Zeppelin a d Pearl Jam sessions are covered. As well their voicing and detail means Norah Jones will be well served also. There have been lots of very good speakers recommended, all with one or two strong suits, but none overall are better than  MA S 500 7Gs. 

randybrinkman what is your room size? The Charney Audio Maesteo will fit your budget and work very well with your gear.

http://charneyaudio.com/pricing.html

Tannoy...if you bought it from Upscale, surprised he didn’t try and sell you a pair..

A good used pair of Goldenear towers would be my vote. I’m very happy with my PL EVO 300i and GE one’s. 

@soix 

Man I wish those Devores were in Chicago.  I'd probably jump on them!  

@pkatsuleas Well, for $200 shipping they could be in Chicago. 🤔😜

I think I’m going to go with the KLH model 5.  The reviews are positive and I really like the look.  I know these aren’t as high end as most of the suggestions above.  

I’ve had several speakers with Primaluna gear, to include Tannoy, Magico, Harbeth, YG acoustics, Revel, and Focal. The best synergy has been with the Focal Kanta range. These easily open up with a little power. The Kanta 2 used might be a little more than your $5k budget but are really nice with the PL. I have the Kanta 3s with EVO300 monos, and even one EVO300 in stereo does just fine with them.  Used YG acoustics Carmels are around $5k or under, and also worked very well with the PL gear.  They are very small towers, depending on your room one or the other speaker could be a better fit.  

I'll be a little iconoclastic here.  Have you thought of point source speakers?  They often image better.  The KEF LS 50 Meta is a pretty surprising speaker.  The wireless version drives the price up, but you already have amplification so don't need the W model.  With a good pair of stands (surprisingly important) you can still have enough left in your budget to pick up a quality sub.  Any floorstander under $5k is struggle a bit at the bottom and benefit from support anyway.  You don't need to blow the whole budget on the main speakers.  Just a thought

I have replaced my Rega RS5 speakers with Audio Physic Sitara 25's.  These are mostly driven by my Cayin CS55A, somewhat similar to the PL EVO 300, made in the same factory.  I use EL 34 tubes and the combination is very good with exceptional soundstage in a small, 4.5 x 3.2 m room. The Rega's were thin by comparison, with a tad more bass perhaps but neither as natural or as well integrated.  Mids are to die for and top end is clear, a little brighter but far more focussed. Any of the smaller AP floor standers go well with tubes in my experience.