Remove the nut compleatly, and spray down with the penetrant of your choice (WD-40, Kroil, PB Blaster - even Air Tool oil and ATF will work well here.) Get a wooden block, and tap it inward just a touch - all you really want to do is start it moving.
Once it moves, take a couple bits of flat metal stock that will fit behind the switch assembly (the whole thing - the threads for the nut are tapered...) and gently prise the thing loose. Once you get it started outwards, it should come easily. If the shaft it rides on is crapped up, clean it before you do anything else.
This is how I removed my NSS assemblies - 87 and 89 XJ. The nice thing about the flat stock is that it will limit the force you can apply - it will bend if you do too much. I think I used about 3/16" steel - you can pull on it gently, twist it back and forth, and such - and it will eventually come loose.
Take your time - you don't want to replace that $300 part!
The only change to the writeups I'd make are the following:
Use a VERY THIN and VERY LIGHT bead of RTV black when you reassemble, on the mating surfaces of the case halves. "Better out than in" - you don't want to use too much, and you can always wipe it off the outside. This will help reduce/prevent contamination later.
Use never-seez on the shaft ONLY when you are putting the NSS back on - NOT on the nut! This will make it easier to take down the next time.
Use some Dielectric Grease on the wiper surface - this helps reduce abrasion and contact wear.
I might still have measurements for the contact blades somewhere - I've made new ones each time I've rebuilt the NSS - but it's been a few years since the last time. I was able to make them from hardware-store brass sheet stock, which worked well (like copper only a little tougher.) I'd use copper or annealed brass sheet - NOT bronze! Bronze is harder than copper, and will wear out the terminals you CAN'T replace!
One more thing - once you have the screws out, put the switch and your hands in a large bag, before you take the halves apart. Who do you think I ended up making new terminals the first time? Don't lose those little coil springs, either...
5-90