I'm very new to this kind wiring, so I may well be corrected here, but I would double check that you have all the earths from pick up selector to the tone pots. From what I can tell, the diagram as shown should allow volume control on both pickups when the central position is selected.... I think.

In regards to the necks, in the central position you should have no output. Its either one or the other or off going by that diagram, which honestly seems sensible, but I guess if you wanted to finger tap on both necks at the same time that would be a problem. I'm not entirely sure how to solve that as wiring both necks would mean using one or other of the volume and tone controls and might mess up their normal operation - unless you introduce a second switch for that scenario.