Wanting to narrow the field for compatible speakers

Have Eric build you some Ulfberhts with all Be tweeters, Duelund caps, Goertz inductors, Path Audio resistors, and Kimber 4TC. There should be plenty left over to put them on Townshend Podiums. Put all those other speakers to shame. To shame.

Eric is at this very moment reading this, smiling and nodding and saying, "Yeah, they would."

What improvements/changes are you looking for?  New or used?

I would echo @soix questions and would also be curious if you can tell us a bit about what you like in terms of sound.  There are a ton of speakers available in this price range and the speakers you have are not exactly mediocre.  For example:

Vivid Kaya 45s
Avantgarde Zeros
Wilson Benesch Vectors 
Stereokonzept Model 2
Perlisten S7t
Raidho X2/X3 or C1.2
Vienna Acoustics Liszt
Canton Reference 2K

These are all radically different sounding speakers that are on (or near) your budget and will sound and look very different than what you have.  I could probably come up with another 20 different speakers.

What I can't say is that any of these is inherently better than your Sophia 3s, just different.  I love all of these speakers for different reasons.  The question is, exactly what do you want?  Are you open to adding subwoofers?  How do you listen, dB level, focused or are you up and about?  etc...

I did the same thing last year. I had a pair of Wilson Sophia's and I decided to get a pair of Focal Sopra 3's.

I know Wilson speakers are supposed to be very musical but for me they just seemed a little slow and not very resolving. The Sopra's are the exact opposite. They are very quick, they are extremely resolving and their mid-range is just phenomenal.

Before I bought the Focals, I listened to a whole bunch of different speakers everything from far more expensive Wilson audio speakers to Legacy audio.

When I listen to music now I actually hear everything... I missed so much detail for this last decade plus.

Sure Mr Rebennack, forget about archaic dynamic drivers and leave crossovers behind. Get Sound Labs 545's