Full Range under $5k-ish

@audiotroy 

1: How big is your room?
19x29
2: How far do you sit from the speakers?
normally 10'
3: How loud do you play?
All over the place. Depends on if the kids are around. 
4: What kind of music do you like?
I listen to a large variety of music. Mainly classic rock, i.e. Floyd, Clapton, Supertramp, Judas Priest; with some newer stuff as well.
5: Is the visual look of the speakers important?
It's important to the GF and a little bit to me. 
6: How far or near to the rear wall would the speakers go?
Currently the DefTech's are 18" from the wall. They could go closer but not much further. 
7: What don't you like about your current speakers?
I like the range they currently have, specs say down to 17Hz, although I'm not sure how true that is. 
8: What are your current speakers?
Definitive Technology BP-2002TL
9: Do you value musicality or accuracy? Meaning would you want to hear more detail out of your system or is your system a bit too fatiguing?
Detail is always nice. I'm not sure I fully understand this question though. 
10: How important is deep bass?
Bass is important as I'm not running, nor do I plan to run, a subwoofer. 
11: What criteria would be in your dream product?
Something that fits my budgets and will continue to impress me sonically. 
12: Are there any loudspeakers make model or brands that impressed you in the past?
Focal and Wilson Audio have both impressed me. That being said both are out of my budget, even on the used market. 

@gregm  I am open to used speakers and I don't need to match the DefTechs for say, just want to make sure I'm actually upgrading. 

@dbphd not completely down to 20Hz but that wouldn't hurt. 

Thank you everyone for the responses.
I didn't think about bringing my amp with me to audition. The only thing that turns me away from that is that I currently Bi-Amp and don't want to disconnect both my amps to bring them with me every time I go to listen.
 

Vandersteen 3A Sigs would be a good choice at that price point.
Audiotroy (Dave) does not like them because he does not sell them. Or maybe he feels they are not up to his standards for loudspeakers in that price range. WHICH is just his opinion.

Here's a demo pair of Nola KO2s from a dealer who is apparently selling off inventory.  No offense to your Def Techs that are very good speakers for the money, the KO2s will bring you to another level entirely on every level.  The reason I'm recommending them is that they're overall awesome speakers, and the mids and highs are dipoles, which will image more like your speakers that I believe are bipolar.  These were $14k retail new, and you can get this demo pair for a little over $4k presumably with full factory warranty.  Buy these and thank me later.  If for some insane reason they don't absolutely blow you out of your chair you can probably sell them for a profit.  Maybe to me if I can get the wife to loosen the screws. 

https://www.upscaleaudio.com/collections/nola/products/nola-ko-loudspeaker

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