Best full range loudspeaker for the used price of 10 to 13,000 dollars

You can likely find a pair of used Vivid Audio K1s in that price range. The K1s changed the game for me. I updated up the Vivid line, but the K1s took engagement and disappearance to unexpected levels. They are also very forgiving to placement and have an exceptionally wide sweet spot. Value is exceptional at regular prices, but at used prices they are really worth considering. 

I second the Olympica IIIs.   If you like musicality over analytical/detail, the Olympicas offer a rich musical sound I've yet to see hear in that price range.  Very non fatiguing sound and fantastic with Jazz, classical, acoustic rock, etc.  Wonderful midrange is the Olympica hallmark in my opinion.  Doesn't hurt they are one of the most beautiful speakers aesthetically as well.  There are some used pairs available on audiogon and USaudiomart depending on where you are located geographically.

If great dynamics and power handling along with clarity are your thing, the Vapor Audio Nimbus black or white speakers would be about that range new.  There is a pair on the east coast for sale at $7500.  They just went off but will probably come back on.  If you were so lucky as to have a pair of Vapor Joules come up used, they would have even better sound.  The Nimbus is a funky cool looking speaker with a whole lot of live sound to it.  The finish on all Vapor stuff is gorgeous.

I will not tell you about what I think or hear say, will just tell you about what I know.
Best fullrange I know is Tannoy Westminster GR, but good luck with finding a second hand pair for $13,000.
Many stated in threads here are good, but one beats them all without the shadow of a doubt in my opinion and would beat many at over $25,000, it is the XTZ Divine Alpha. Just plain amazing for the price, $8,000 new. Swedish stuff, all first batches of production are pre-sold. These will absolutely dazzle you or i know nothing after 30years of audio mania.

"THE BEST" in speaker performance is subjective. To properly compare A vs B variables must be controlled. Ideally listening should be blind where the listener has no idea of the brand or physical characteristics. Connections are made to the same components with the same interconnect. Comparisons are done quickly to eliminate the loss of acoustic memory we all experience. Ultimately the goal should be to accurately reproduce the original image. Achieving this goal results in a satisfying experience as the listener is exposed to to new and different types of sound. The speaker should be relatively tolerant of its environment. REVEL has a custom platform allowing them to quickly compare speakers using the above guidelines. With this in mind the REVEL speaker is an excellent place to start. Vast R&D resources, (Harman Luxury Audio Group), and excellent guidance from Director of Technology Kevin Voecks, result in a superb speaker at all price points. Voecks has an outstanding pedigree and the results are evident.
Nuff Said.