$3500 floor standing speakers used. What would be your choice ?

Speakers are really tough to recommend as they are such a personal choice based on what sounds good to you.  The room, electronics play a big role in how the speakers sound with synergy also playing a huge role.  The right amp paired with the right speakers can sound very different than an amp that really doesn’t pair well with a particular speaker.  
 

That said, based on what you’ve described as the sound signature you like, Sonus Faber, DeVore, Spendor, Legacy would all be brands to look at.  Golden Ear though different in design also would likely be a really good fit.  

Paradogm, Focal are outstanding speakers but fall into the highly detailed, chasing that Hifi sound you mentioned not really liking.  BE tweeters are amazing but often are implemented in a way that leans into the Hifi sound as well.  

I’ve had BE Tweeters, several Focal floor standers and ended up landing on Alta Audio Alec’s which would check most of your boxes.  The Seas kit also would be right up your ally, sound like a perfect fit to what you are after.  Omega DynaTen speakers also would be worth a look. 
 

Good Luck, 

excellent choices. I have a few speakers and I would narrow down to these 2- both American (I am not).

Omega- single driver speakers. I have the Junior 8 XRS. Even new they would be within your budget. For me they are almost the best speakers I have had, besting even stuff more than 2x their price.

Devore Fidelity Orangutan Baby. Used they could just be within your budget. Again amazing sound.

A third one- which might not come within your budget, used are from Poland. Qualio Audio IQ.

Rosso Fiorentino Elba 2. 

Used Devore Fidelity Gibbon 88 US audiomart has a pair $2450.00

A lot of advice provided in this thread...

Because you have a really nice, clean and simple system - Nottingham into your VAC integrated (love that amp, and I am vinyl based also). I think match the integrated to the speakers (think 93bd and up), and the speakers need to match the room...

But my experience says go for something like the Focal 1038. It is as good as the Sopra's 2 or 3 IMHE, with bass more like the 3. Easier to drive with tubes than any Sopra (I have heard them just Rock out (loud) to large Brahms or Miles KOB on as little as a 40w AudioPrism EL34 amp in a 12x27 room). The 1038 is a large speaker system, but small enough for a good match with your integrated, will fit a lot of rooms.