Full Range under $5k-ish

OP, as an x owner of first the P3 then upgraded to the P5, I felt there was better value to be had in their price range, but the P6 might be  whole new design upgrade. Dunno. May not be that big a deal spinning just vinyl

Parasound is pretty accessible to speak with whether the P6 uses the same phono as your P5

anyway, speakers. My room is ~1/3 bigger than yours and yet my Emerald Physics KCIIs are doing a bangup job with my kit. They're barely 4ft tall, slender semi pyramid shape, open baffle. I have 2 SVS Ultra subs which are turned off as I have ample bass without them. They are running  a special (or often do) for $1499. Run don't walk. Live happily everafter

PMC twenty/23 or twenty/24

Demo some of the larger Ushers and ATC SCM 40 and bigger if you can

OP, I appreciate the inconvenience of disconnecting your amps, but consider bringing just one amp and biwiring to get virtually the same performance.  A Carver TFM-35 is a powerful amplifier and doubt that the impedance characteristics of your speakers' high frequency drivers present any meaningful stress.  The TFMs have a distinctive sound (after all, TFM means Transfer Function Modified) and so it seems all the more important that you test the speaker/amp interaction.

My two cents.  Wishing you well!

As most know, I am a Vandersteen fan. 
And, you might ask, why so many have recommended them?
Because they outperform for their price range, and are very listenable. 
But, that is your choice. All I and the other posters want is to guide you to something that we think would be a good move from your current speakers.

For under $5K, you could get a pair of 3a sigs with a pair of 2w/wq subs and be pretty close to a Quatro.
A more attractive option would be to get the Treo's plus subs, but that is probably a bit more than your budget.
Either way, you would get a full range speaker system.
If you let us know your location, maybe we can direct you to a dealer.
Bob