The pickup ring should currently sit around the outside of the pickup rout. If you move the neck further into the body, you'll loose the little edge by the neck that the ring sits on and the ring will be sitting off-centre. The pickup routs on those kits aren't the most generous - especially for after-market pickups which seem to come with wider tabs than the PBG kit ones - so you'll probably need to do some enlarging to get the pickups sitting well in the routs without touching the sides.

Have you checked the neck measurements yet? No point putting it together with high-value hardware if there's a dodgy fret installation.

On to that harness:

You are going to need to bend those capacitor legs so that they both face outwards, otherwise they'll be right under the f-hole and very obvious.

You'll still need to make up a bit more of the wiring harness yourself, for the jack and the pickup selector switch, so still use a bit of cardboard to do it so that you can minimise wiring lengths. Some wiring will need to run around the outside of the pots as you'll still need to keep the U-shape of the existing harness to avoid wires running across the f-hole. The harness is designed for a LP, so the hole spacings on their plastic sheet may not correspond exactly with those of the kit.

And you may have a really hard job (possibly impossible) getting those pots in through the holes. They are very tall and when you come to fit them, the whole height of the pot, including the shaft, will need to fit almost upright the body space. You can angle them over a lot to start with, but when you come to actually trying to pull them through, they will need to be almost upright to do so. And at a slight angle, they are still almost as tall overall because of the switch body.

Measure the total pot+shaft length (without its knob attached) and compare that to the thickness of the body at the two bridge control pot hole positions, taking off 10mm (2x5mm) for the thickness of the wood, to give the height available to you to work in. If you've got room to spare, then good. If your a couple of mm short, then you just might do it (with a lot of swearing), but anything over that and I don't think you'll do it.

I've got a 1995 JP Model LP with that set-up, and I occasionally use the coil taps (to avoid swapping guitars) and only use the 'pickups out of phase' switch if I am doing a Peter Green track that needs it, but could live without it (it is a very thin and quacky sound). I never use the parallel switch (or whatever it is) on the bridge tone control (very weedy sounding). So if you find that you can't get that harness installed, you could try looking at getting a couple of standard pots and a couple of switched pots just for coil tapping (which should be a much shorter overall length) and just have (what I think are) the most useful features. Then buy a LP kit and fit the JP harness to that, as it was designed to do.