Looking For A New Tube Integrated Amp With Very Specific Features

Triode Corporation (Japan) makes a $5,000 integrated with remote control of volume and mute, a headphone jack, 300b single ended triode.  The only thing missing is that its inputs are RCA, not XLR  I have not heard it, but, I've heard other stuff that they make and they are pretty good, particularly for the money.

https://triode.co.jp/english/TRV-A300XR/index.html

You might consider reaching out to Aric at Aric Audio. Currently, all of his excellent offerings do not include an integrated, he might be able to build something bespoke. Perhaps Aric will see this and reply with the possibility...

Tektron Audio (Italy) has a line, the TK Two Integrated, that has numerous parallel SE versions with a variety of tubes.  Not widely distributed, but good reputation.  Fezz Audio Lybra 300B, much easier to find.

As for ease of biasing, consider amps that are “cathode biased.”  This means no adjustment needed, but at the expense of not getting the most power out of the tube.  But, on the plus side, cathode biasing is generally gentler on the output tubes.  This is not necessarily something employed by cheaper amps.  Audio Note, for example uses this approach on their amps which are pricey and very nice amps.