0.01uF is not a very large value for a coupling cap, .02uF to .1uF are very common in many classic guitar amps ...
The output 6EU7 has a 0.01µF which sees 470kΩ plus some resistance from the pot before. 0.01µF and 470kΩ is -3dB at 33Hz.
2) I would not change the coupling caps to a smaller value to expect a brighter outcome at the expense of your lows and low mids. ...
This is a good point.
Try tacking a series resistor-cap across R12, maybe a 1kΩ in series with a 0.1µF. The goal here is to see if this causes a treble boost at all; values can be tuned later.
3) A more reasonable solution would be to put bypassing caps one at a time to see how and what each does on R5 & R11...
We can't do that, as it would kill the dry signal through the reverb. Look at the Normal control, then pretend the added bypass caps are a short to ground.
In my suggestion above, I'm uncertain if there is feedback as well as normal-signal feed-forward. So I honestly don't know if the paralleled cap will add treble or cut treble. It could be tried, and if it cuts treble (because of feedback action), then we'd know to use a cap-to-ground in this path between R12 & R13.
But in the end I suspect the savings of an extra 9-pin socket & circuitry of
Fender's 6G15 forced a compromise which is giving this dark-verb result.
Of course, we could just take it for what it is (especially in a vintage unit), rather than ask it to be a 6G15.