L.s.d

[Conkers]

Strewth.... it doesn't matter if it is a live axle or not,

First measure the backlash on your s12, (backlash is how much the crownwheel rocks on the pinion. Keep a note of this as you are going to use the original crownwheel again on your lsd.
Then you remove the guts from the kingcab rear axle, remove the crown wheel and bearings and throw away everything except the diff cage (with plate type lsd).
Then.. as long as you have the same bolt diamters, (apparently some were 10mm and some 12mm) fit your original crownwheel from your original non lsd (or gay viscous) rear axle onto the kingcab plate type lsd guts.
Fit the bearings, check bearing preload, check the backlash, moving the shims around to get the same backlash as you ran with your standard diff, otherwise it will whine...

And bobs your uncle...

Conkers <--- thats all I got to say about that.

[30psi]

Yeah I know how to build a diff, but from when I've seen the other Nissan axles open (H190 for example) they seem pretty different.

How do you know if the crown wheel will bolt on or if the bearing diameter or bearing cap diameter will be the same though? I agree that with shimming the diff you aim for the same backlash, but you also need to check the pinion depth. My point is for average joe bloggs with an s12, doing all this will be a major pain. My advice is to make things easier for yourself and stick with an option i've mentioned previously.