Tube screamer "clean mix"?

[Rob Strand]

If you're introducing a variable in an equation, introduce it ("Hi! This is Id, they're the current through the feedback diodes!"?). If you don't, it just appears

Very true.   That's actually something I have a beef with about modern papers.   In some contexts it's obvious but in others I doubt the author would remember a year after writing the paper.

[PRR]

I don't see how you smart-guys are confused.

What is the gain for very small signals? Some large number set by resistors the usual way.

What is the gain for large signals? It becomes a plain Follower (Gv=+1).

Work it out on paper.

Work it out with DC: an opamp and a pot to give variable DC input voltage.

In the sim below, small signals gain-up by factor of 11 (mis-typed as 10).

When the voltage across R48 exceeds a half-Volt, the diodes turn into shorts. Gain is just unity.

No assumptions of diode-knee or opamp supply are needed. (These determine details, not overall action.)

On sine-wave drive, small signals are boosted at high gain up to diode voltage, and then follow the input with that voltage offset.

[Rob Strand]

I don't see how you smart-guys are confused.
...
No assumptions of diode-knee or opamp supply are needed. (These determine details, not overall action.)

I'm not confused.  I see your way as well.  The analysis I gave only shows that to be true.

You get a similar situation with a cap across the feedback resistor.   The non-inverting amp with a feedback resistor + feedback capacitor isn't quite a true low-pass filter as the gain always levels to 1.  If your gain is 100 overall it looks a like a low-pass filter but if your gain is set to 2 then it only going to give you a -6dB shelf since the output can't get below unity gain.