What to buy?

Wharfedale Linton 85th Anniversary w/ stands $1498.00

Because of the high sensitivity of the Klipsch  Cornwalls ( 102dB @ 2.83V / 1m ) and Klipsch Forte III (99dB @ 2.83V / 1m), I usually associate them with lower power amplifiers primarily of the tube variety.  Since the OP  Emotiva XPR5 is 400wpc, I wonder how well efficient speakers perform with above average powered amps.

Somehow, you need to change the dimensions of your room. Having a square room, you’re already starting wrong from the gate.

I’ve listen to the LS 50 and R500 and for the Classical music I listen to, there is
a significant jump up with R500 .

If you aren't the tweaky audiophile type who values space and imaging above all you might look at Klipsch.  They are really fun speakers and can dig out something good with even the junkiest of recordings.  I have the Forte III and in many ways enjoy them just as much as my Kef Blade 2

Save a little longer and get Klipsch Cornwalls. Add subwoofers down the line and you'll easily hit 115 dB and have the remarkable detail and dispersion of horns. For medium powered amplifiers there is no better speaker for a rock and roller. 

The R700 might go 1 or 2 Hz deeper-that’s. it. Not worth a 33% increase. Everything else exactly the same.

I've listened and compared the KEF LS50 (which has numerous very  favorable reviews,,,and sales...) to the KEF R700 and to my untrained ears they sounded very similar with the exception of more bass for the R700.  I'm guessing the R500 is cut from the same sonic cloth.  Maybe a used R700?

+1   R500 is as flawless a  speaker as I have heard .

KEF R500 on closeout or used are very detailed speakers that sound like you are in the audience with very excelent bass - no subwoofer needed, are built incredibly well (the built in mini-stands are included and are perfect for any surface). Unlike some others, they look like they belong, nice and slim and deep. 

Agree with the used Vandersteen 2CI.  Tough to beat at your price point.

I'm a fan of Magnepan and Emotiva too. I owned Magnepan MG-IIIs for 20 years and decided an upgrade was needed. I found used Magnepan 20.1s for $5500 (new $12,000) and couldn't be happier. Your amp will have no problem driving any of the Magnepan line due to the power at 4 ohms. I don't know what can be found for $2000 because I haven't really looked.

GoldenEar Triton Five or Triton Seven (Triton Three+ $2,750.00/pair). Good-great sound.  Favorable reviews.  Designed by seasoned Sandy Grossman (just retired recently).

Tekton - an acquired look but the sound punches way above their price

As previously mentioned, at $2k there are a large number of speaker choices coupled with frequent new model changes and updates (unlike say a $30k speaker where you can narrow your search to less than a handful).  I suspect that us forum members can give you great choices, but is actually too small a sample of what is actually available.

As long as you've done your homework, I believe purchasing a $2k speaker without demo isn't too risky - you'll not get a bad speaker, rather, you'll get various shades of good-great.

My suggestion, simply because this is what I have, Martin Logan Motion 40's. They have a newer model out now but I think you can still find the Motion 40's, new, at a reduced price that should come under $2k.

Mine were $2K when new.

Do you play a musical instrument?  For piano and violin either Magnepans or Martin Logan electrostats seem to have the midrange on up better than cones.  

Maggies and MLs difficult to beat for clean pure mids and highs. On some models a sub might be needed for deep, solid bass.

Elac Uni Fi

What are most important things to you sound wise?  What aspects of speaker performance are most important to you?  What don’t you like?  If you’re not really sure about these things I’d highly recommend going out and listening to anything you can — it’ll be well worth traveling a bit BTW —so you can better identify these types of personal preferences.  Without this info it’s really not possible to make a recommendation with any confidence that it’ll sound good to you.  Nobody here, no matter how experienced, can tell you what you like as, especially with speakers, personal taste is a huge part of the equation. 

Check out Klipsch!!
https://www.crutchfield.com/shopsearch/klipsch_floor_standing_speakers.html

I have used Emotiva amp with Magnepan 1.7 and really enjoy the sound delivery, dynamics and soundstage openness of the combo. I highly recommend the Magnepan 1.7s. 

Focal or Paradigm

Many don't think of Magnepan as a rock speaker but you need to hear them for yourself. I loved my 1.7i playing rock you'll get clarity and pinpoint instrument location in the sound field if you find a used pair you'll have enough to add a sub.
Whatever you buy be sure to do plenty oy auditioning first as each speaker has its own flavor. Also be sure the Emo can handle 4 ohm speakers.
Enjoy the search. I made many new audiophile friends by posting for home auditions. Hopefully we'll get rid of this virus and can start getting out again.

Call John Sollecito at Source Technology and talk to him about the 7211’s. Great American made speakers at a good price. John will make you a good deal on them I’ve known John for for 40 years. You can tell him Jackie said to call. If you have $2000 to spend you owe it to yourself to talk to him. I listen to classic rock very loud 95db’s +. And the 7211’s deliver. I added two subs to them but you can do that down the road. Call John at (860) 918-3088. 

cerwin vega xls 215 

Polk LSIM 707