Full Range under $5k-ish

lots of options in the under 5K category.   Another consideration, hold on the speakers, put 3K into your source gear, arm, cartridge, phono preamp and spend 2K on speakers.  Feed as much music to the last element in the chain.  You can a lot of cartridge for $700-$1000 - e.g.  Hana and Ortofon,  I've heard really good things about the Parasound JC3 jr. phono. 

Also if you haven't done some room analysis and treatment, lots can be gained there as well.  Great gear in a poor room never reaches it's potential. 

Lastly - Vandersteen's and others present some interesting biamping options - with solid state for the bass and tubes for the mid/highs. 

My first thought was the Revel f208, but I personally would look at the Usher Dancer 2 or one of the larger ushers used because they seem to be more amp friendly. 

See if you can get your hands on a pair of used Anthony Gallo Acoustics Reference 3.5 or 3.1 speakers.  They are remarkably "full-range", and remarkable performers, considering their price (MSRP and on the used market).

Also, check out the GoldenEar Technology range of speakers.  They are very well reviewed and also seem to have a goal of presenting a "complete" frequency response.

My 0.02.  Enjoy the search.

Philharmonic Phil 3.  
25Hz at +/-2dB (Also, it states 85dB sensitive, but it’s actually 88dB sensitive from 30Hz and up).

Motorman is right . Do yourself a favor and listen to a pair of Bache audio tribeca 001.
I was at the NY audio show in Nov and there were only 2 rooms that had exceptional sound. the Harbeth room auditioning the m.40.2 at $15,000 a pair / and the Bache audio room auditioning a pair of tribeca 001 at $5500 a pair.
Two completely different sounding speakers of course. But wow it was nice to see/hear someone who knows how to make a full range speaker.
Fostex super tweeters at $1000 a pair,who does that !!
Anyway based on your stated music preference the tribeca’s will easily out perform anything else in your price range.
Good Luck