Best phono stage balanced under $3000 used

The Basis ASR Exclusive has been going for just a little more than $3K, used, and it truly is a world class phono preamp. My friend upgraded to this from the Aesthetix Rhea. (The Rhea was very good, but not quite in the same class, as the Rhea had a bit of tube noise that was distracting during the quiet passages. However, the Rhea is the most user friendly Phono Preamp I know of.)

The Clearaudio Balanced Reference fits your needs at used prices. The K&K and Ayre list new for less than $3,000. All of these will give you excellent, but not state of the art performance.

Throw some NOS Telefunkens and/or Siemens into the unit and the noise floor of the Rhea drops considerably. I agree the stock Sovteks are miserable. Unless I crank the gain and volume way up, my unit is rather quiet. Tubes add a sense of air, realism and palpabilty which will be absent from solid state phono amps.

K&K Audio sells a phono preamp kit for about $1500 which offers balanced as well as single ended topology. I own one. In my opinion, it is much better than the EAR 834p.
Perhaps you should consider the K&K kit; then take the money that remains in your budget and upgrade your cartridge. I suspect the improvement from those two purchases would exceed the improvement from any phono preamp you could buy for $3K.

There is also the Trumpet.