looking for a Integrated amp $6,000 range

Not sure if your preference is for SS or Valves but I can certainly recommend a used or discounted Ayon Triton III with its 8x KT150’s and Triode/Pentode options.

Amazing tech and build quality, maybe check the manual out online for an insight.

I’ve used it with Harbeths, Escalante Fremont Mk2 and Tannoy Arden Legacy’s.

Ayon Triton III does the business, try and hear one or if taking a risk, it’s minimal taking account of its quality although I imagine a few of the suggestions here fall into that category.

Remind me what your speakers are?

Lots of great choices here.  I love my Mimas.   
Good luck.  

The speakers I’m using are the
 Legacy Focus 20/20 late 90s version 

Hegel is a really top grade amp, comes with a DAC, which is audiophile grade, and the headphone amp is in many models, the amp output. Plenty of analog and digital inputs. I own both the h190 and h590 in my two systems. Playing into the Dynaudio evoke 50 the h190 and the monitor audio gold 300 5G, the h590. Outstanding value...

Strong recommendation here for the VAC Sigma 160i, or better still, the SE version. Available used in your price range, depending on options.

With speakers as sensitive as yours, the 85 watts per channel would be very generous.

This is a MAGNIFICENT sounding integrated amp. I'm powering Nola KO speakers, 89 db sensitivity, and the power is plenty. Carl Marchisotto of NOLA recommended it and uses it to demonstrate his speakers.

Before the VAC, I had an Audio Research VSi60 -- also a wonderful amp, also recommended by Carl M, and available used these days for under $3,000. The VAC has a bigger sound, better bass, kind of more of everything.

It's available with or without a MM phono section, and with or without balanced inputs. Mine is an SE and has both options. I used the PS Audio Stellar phono pre, though, which absolutely wipes out the VAC phono.