Corrected the cap... would be grateful to have someone take a look to see if this will work. I suppose that there is no rush. I started this project in about 1986...
Yep, that should do what you want. To help reduce possible noise when the neck is in south-single mode, you may want to switch the Neck North Finish link to the rotary via the push/pull too so that the north coil is not 'hanging' when the push/pull is up.