Upgrading pre amp advice.

Unity Gain Designs are extremely transparent and not producing an overbearing upper frequency in any way at all.

A Valve Pre' will have quite noticeable tonality is compared to a Unity Gain. 

A AVC or TVC will also have a noticeable tonality when compared to a Unity Gain, but will be lesser than the Valve influence on Tonality. 

This is my experience of being a Valve Amp user of more than 30 years and a Slagle AVC owner for 10 years. 

I have no issues with Tonal Influences from recognisable Rich Tonal  Influence, through to perceivable Transparency. In recent times, I go to the Transparent Influence, more than a influence from a hint of Rich Tone. 

@vthokie83 ​​@dogearedaudio : I took a look at the website of Tubes4HiFi (really interesting, but none them where balanced)

@jdub39 : thanks for this additional info

Someone experiences/reflections on the SPL Selecter??

@vhond 

I am not familiar with your Bryston (or much of the rest of your rig for that matter), so I make these suggestions with caveat...

Might be worth looking at a used Zesto. I have several clients that have these and love them. The one I’ve heard was excellent. There was one I was considering on US Audiomart not long ago within your budget, I think. If I remember correctly it had balanced in’s and out’s.

Might also be worth looking at a VAC Standard Preamp. There was one with a phono stage on Reverb for $2K. Not balanced I don’t think but a very nice pre-amp for the price. You can sometimes see the VAC Renaissance pre-amps pop up that are still relatively close to your budget.

Good luck.

You might also consider the Pro-Ject Pre Box RS2 Digital, which has a small form factor yet has dual ESS Sabre 9038 DACs, a solid-state headphone amp, a selectable tube output stage (for speakers,  solid-state also selectable from the settings menu) with 4x 6922s, a relatively large choice of filters, remote, I2S for connection to ProJect's premium CD transport, digital inputs AES, S/PDIF coax and optica (2)l, USB, BT, and analog inputs, XLR and unbalanced. It is in your budget. The casework is aluminum plate. I have two of these now, one in service with Buchardt actives and the other with passives and a NAD C298 Purifi power amplifier. 

You are from Europe, so many of the suggestions make no sense as the brands will not be available here. Better look for high-end German, French or Italian brands used, like Symphonic Line, Valvet, Gold Note, YBA. Recently I bought a used MFE Tube One SE preamp for a good price. Couldn't be happier.