Firstly, here is a diagram that utilises three three-way switches:
I'm a shade confused as to why the black wires from the pickups are being treated as the hots rather than the grounds, but I'm not sure up to speed with Seymour Duncan pickups. The diagram simplifies stuff to the extent that each neck has a single volume and tone control only, and the neck selector switch simply switches between necks prior to the output jack. Think of it as two Telecaster wiring schemes, complete with two pickup selector switches, that meet at a final switch that governs set of Tele controls is sent to the output jack.
I'm looking at EDS 1275 wiring diagrams online. A few people get round the issue by using three switches; one to switch pickups for the the first neck, one to switch pickups between the second, and then a final switch to switch between necks as per above. This means you can use the more readily available Les Paul-style 3-way switches going around.
With the switch you drew up there, six terminals isn't enough. You need twelve if you follow my diagram, set up in four banks of three terminals. With the switch you've currently got in the 4080 you can switch between each pickup pairing, per neck, but you have to solder the hot wires for each pickup pair together. However it seems that Switchcraft pull it off with only nine terminals, using a switch like this: which you must have used in your Gibson:
Without a multimeter I don't know how easy it would be to map all of that out. Four terminals will be taken up by each of your four pickups. You then need to work out the common terminals for each pair of terminals. For example you need to work out the common output for the two terminals that will cover your two neck pickups, and do the same with the bridge pickups. This is why a meter is handy! The Switchcraft is covering the functionality I outlined with the generic switch in my post above, and it is a guitar part rather than a generic electrical component.