List of desired features:The LTA MicroZOTL preamp appears to check all your boxes. Looks like you can drop the gain by 10db, from 10-12db down to 0-2db. No balanced output, though.
<6dB gain
<500 ohm output impedance
tubed output
at least 2 sets of outputs
balanced in/out optional
https://www.lineartubeaudio.com/products/microzotl-preamplifier