Guitar Treble Bleed, Part 3: Problem with 3 pickup, 3-way-switch circuit

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The Epiphone Riviera P93 guitar has 3 pickups and 3-way selector switch. The only way to turn off the middle pot is to turn its volume all the way down. Because of this, the volume pots must be wired with independent (decoupled) wiring, which results in bad treble loss when turning down. And as shown in this video, there’s no way to use a treble bleed cap since turning down one will result in loss of high frequencies in the other. This problem can be avoided on a typical 2-pickup 3-way switch (traditional Les Paul style) guitar since it can use non-indendent (coupled) volume wiring.

In this video, I demonstrate the problem on the P93, then draw up a circuit diagram explain why it's happening.
For more background on treble bleed, selecting caps, and installing, see parts 1 and 2 of this video series.