Ok Kurt, as per the PM here's an annotated diagram to help with the coil spit mod:
As I've said before, be very careful handling and/or moving the pickup's wires as it doesn't take much to break either the connections to the coil wire or the coil wire itself.
I know your new shielded wire is 2 core but we only need one of them for this, so pick a colour and just ignore the other one. Cut to length, trim and strip the tips as needed to get it to line up with where you need it to make the connections.
You don't want to cut the series link wire (black), you just want to pare enough of the insulation off so that you can join the coil split core wire onto it (essentially, you are tapping onto that wire). Very careful use of a sharp craft/x-acto knife works well to remove some of the insulation. Once you've cleared a small gap in the insulation on the series link wire carefully solder your coil split core wire onto it.
The coil split shield wire connects to the existing pickup bare shield wire (ideally where it is soldered to the baseplate), so solder that in place too. On these pickups the original shield wire is usually split into two, with one branch going to a coil and the other going to the baseplate. Connecting your coil split shield wire to the baseplate branch is the stronger and safer option.
Once you've made the connections ensure they are insulated with heatshrink and/or electrical tape so they can't short with anything (not so much an issue with the bare shield wire, but definitely insulate the series link/coil split core join).
IMPORTANT: before you put the cover back on the pickup make a note of which coil the white 'hot' wire connects to. In the above image you can see the white core of the original pickup wire connects to the 'slug' coil (as opposed to the 'screw' coil). You need this information for each pickup when it comes to wiring your coil split switch. Check this on each pickup and write it down before you close them up, as it can very between pickups. For example, in this thread the bridge hot is the slug coil and the neck hot is the screw coil.
Once you've got all that sorted let me know and we can work on drawing up a wiring diagram for you with coil splitting to match your coil/hot configuration.
Clear as mud?