the circuit diagram, and wiring suggestions

Here's the switch position diagram again, with the circuit diagram added at the bottom:

This is viewed from the back, of course.

The first step is to slacken the strings on the guitar so that you can remove the pickguard.  Slacken them enough that you can raise the whole bunch of strings about 2 inches over the pickups.  If you loosen the strings but keep them still wrapped around the tuning pegs, you can probably re-use the same set of strings.  After the screws are removed, with the strings slack, you can carefully maneuver the pickguard out from under the strings, to the side.

I'd suggest taking one or more photos of the wiring on the back of the pickguard, before you start cutting and drilling.  (Take some when you're done, as well, before you close it back up, so that if something doesn't work, you can get a clue as to maybe why not, and/or get some advice by sharing the photo, before you have to take it all apart again.)

The pickguard will remain tethered to the guitar by two wires: the output coax to the jack, and a ground wire which presumably attaches to the bridge underneath, somehow.  Be careful not to overstress these wires.  You can probably do everything with these wires attached; however if you're not afraid to re-solder things, you can cut these wires to make your life easier.  Cut them right next to the attachment points on the pickguard end, so you preserve maximum length to reattach.

Clip off the wires attached to the 5-way switch, and remove it.  Take the time to prepare the new ends of the wires you have clipped, by stripping insulation to the right length, twisting the strands together, and then tinning each conductor with solder so that when the time comes, it easily and almost instantly connects to the chosen, also-pre-tinned, lug on the switch, with just a touch of heat from the iron.

The three switches can be wired up as a unit separately, before mounting in the pickguard.  If you bend the wires carefully to avoid shorting, you can wire this with bare copper wire, such as #22 solid.  Then once the assembly is mounted, you can solder on the (pre-prepared) coax lines from the three pickups, and the black and red unshielded output wires.