Maybe, I can help a little.
That last diagram is a typical coil split arrangement. It is not a phase reversal diagram. It's pretty much exactly how I wired the coil split for my LP Studio, except I chose to use the push/pull pots in the volume position rather than the tone position, for more immediate access. I also used 50's wiring instead of modern. The way a coil-split works is that one coil is simply short-circuited to ground.
The difference in the capacitor connection schemes you pointed out is because the top diagram depicts '50s wiring. The bottom one shows modern wiring.
The only meaningful difference between '50s and modern wiring is that in '50s wiring the tone circuit taps off the wiper (center lug) on the volume pot. This is the output of the pot. Modern wiring taps off the input of the volume pot, which is the connection directly from the pickup.
The tone circuit, itself, is a series circuit consisting of the pot resistance and the capacitor leading to ground. Electronically, it doesn't really matter if the resistance or the capacitor is first. The main distinguishing feature between the two tone schemes lies in where the tone circuit taps off the volume pot.
However, getting back to the original idea of doing a phase reversal, the top diagram is showing both a phase reversal and a series/parallel pickup setup. For a simple phase reversal you only need one push/pull pot. I've never tried doing the series switching.
As I suggested earlier (post #12), for a simple phase reversal, I'd ignore that top diagram. Instead, just wire one pickup to it's volume and tone like you'd normally do, without using any push/pull pot. It doesn't matter which pickup you choose. I tend to choose the bridge pickup. However, the second pickup should be wired to the push/pull pot as illustrated below:
Note the comment in this illustration. The hot lead from the switch (that black wire coming from the lower left switch terminal), will get connected to the input of the volume pot. From there, the volume and tone will be wired normally.
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