~$6K mini-monitor recommendations?

What amp are you using and approx what are the distances the speakers will be from the desk/side walls/rear walls? Many of the recommendations you’re getting are totally wrong for nearfield placement close to boundaries!

At least start with models designed for nearfield. From the pro world: e.g. ATC SCM12 Pro (passive), Focal Shape 65 (active).

Harbeth P3ESR or LS3/5as should work, too, being sealed and very small.                                                                              

What about a Falcon Acoustics LS3/5A ??

I have no first hand experience, but they seem fun and suited to the task.

I own the Harbeth M30.1 and the Harbeth P3ESR. I think for your application the P3ESR would be a better fit. I have owned many of this type of speaker, Spendor, Kef, etc. and the P3ESR is my favorite of the lot. The KEF LS50 is not a BBC type speaker.
https://www.bing.com/videos/search?q=harbeth+p3esr+review&view=detail&mid=5D7EB69CCEBBAAE793...

If these monitors are near-field - on your desk - and given your budget, I would look at the line of professional studio monitors by Focal, Dynaudio, and others. 

What do you expect to get that the Kef LS50 can't deliver? I think you will just be throwing money away.

I think the same thing. I am going to both upgrade my electronics to use with my LS50's and also buy a bigger "bookshelf" speaker to keep in the same office as the LS50's,  the Yamaha NS5000. The Yamaha is much better than the LS50's ($15k)  and also has a almost full range sound. Crazy as this sounds I plan on placing the LS50's on Isoacoustic stands and place them on top of the NS5000 when in use, otherwise on a side bookshelf.

I am keeping the LS50's because it is an incredible monitor and I will use it until it falls apart. I do know that better electronics brings out the best in the KEF's.

BTW - If you are set on up grading and like the LS50 sound the KEF Reference 1 is a great choice.