Since I had a few last minutes to contribute to this topic, I’ve done a quick experiment.
I’ve used my Steinberger Spirit with Bill Lawrence PU’s. The bridge one is a vintage L500, which has the same specs than a contemporary L500XL. I’ve plugged it straight to the board, through a 1M input.
Then I’ve played chords from unfretted strings to 12th fret. The charts below stack the frequencies produced during these few seconds of playing.
UPPER LEFT pic shows the response of this bridge pickup with its 500k volume and tone full up.
BOTTOM LEFT pic is the response of the pickup once the Q filter is set @ 0/10. One can see the scooped mids due to this LRC network.
BOTTOM RIGHT is the pickup filtered by the tone pot @ 0/10 (this control being fitted with a regular 0.022µ cap): the peak is located in the low mids (a.k.a. "low mud") and there's no more frequencies beyond 2khz... But it's normal: hey, after all, it's a regular tone pot!
UPPER RIGHT finally shows the same thing BUT now, the tone pot features a low value cap (=2.2nF, ten times lower than a regular 0.022µ component).
In this last case, the frequencies enhanced are twice higher than with a standard tone cap and let breathe the audio spectum until 5khz. This EQing matches the curve produced by many OD pedals (a TS produces a wide round mid boost centered around 800hz, for example).
I don’t know if this rambling answer gives any solution regarding the tone desired but at least, it should show what I was trying to explain in my posts above, about low value caps as mid enhancers.
View attachment 80462
As a side note, I add an explanation due to Bill Lawrence (R.I.P.). It's about guitar cables (whose capacitance acts exactly as if a low value tone cap was permanently enabled) BUT there's some words appliable to tone pots, after the central sentence:
You might ask "How does the effect my tone?"...
http://www.billlawrence.com/Pages/All_About_Tone.htm/CableandSound.htm
FWIW - two cents from this old fart of freefrog.

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