Some quick observations:

First, I'd take out the kit neck pickup and put the Wilkinson in there. There's no need for it if your replacing it and it clutters things up visually.

Something tells me this switch may have been wired backwards as to what I need for the neck to middle to bridge configuration goes...
It's not really backwards, as much as it is just incorrect. See my comments below.

IMO, there is no need to replace the switch unless it is faulty. Installing a Fender-style switch may be problematic with the depth of the control cavity and would unnecessarily complicate things for you at this stage of your build experience.

NECK PICKUP:
The red & white wires from the neck p/u are suppose to go to Lug #6. They appear to go to Lug #3.

The yellow lead (HOT) from the neck p/u is supposed to go to Lug #1. It appears to go to Lug#4.

I can't tell where you're grounds for the neck p/u are going in the pic.

MIDDLE PICKUP:
The red lead (HOT) from the middle p/u looks to be correctly soldered to Lug #2.


BRIDGE PICKUP:
Red & white wires from the bridge p/u are supposed to go to Lug #8. There is currently no wire soldered to Lug #8 and I can't see where the red & white wires are going at all.

The yellow lead (HOT) from the bridge p/u is supposed to go to Lug #3. It appears to go to Lug#6.

Again, I can't see where the grounds for the bridge p/u are going.


SWITCH to VOLUME/TONE CIRCUIT:
You currently have soldered a wire from Lug #1 to the volume pot. That wire should be come from Lug #4.

There should be a wire going to ground soldered from Lug #7. You currently have nothing soldered to Lug #7.