Well, this is embarrassing: my diagram is incorrect. That's why I didn't post it originally last November, I worked on it a bit, gave up, then when I looked at it again I had forgotten the mistake I had made. 
Specifically, the "standard P" config won't work on this diagram because it actually connects L2 and L4 in parallel then had L3 in series with those. It would make a sound, but it won't be hum cancelling due to the odd number of coils.
The bottom line is: with 4 switch poles to work with, you can have a P or reverse P, but not both. The problem comes from having to lift the ground of L4 for the standard P mode. You can still have all coils in series, "quad coil" mode (both series pairs in parallel), "J-mode" with either the north or south coils, and either P or reverse P.
Specifically, the "standard P" config won't work on this diagram because it actually connects L2 and L4 in parallel then had L3 in series with those. It would make a sound, but it won't be hum cancelling due to the odd number of coils.
The bottom line is: with 4 switch poles to work with, you can have a P or reverse P, but not both. The problem comes from having to lift the ground of L4 for the standard P mode. You can still have all coils in series, "quad coil" mode (both series pairs in parallel), "J-mode" with either the north or south coils, and either P or reverse P.
