Hey Jethro,
Have a good search on here mate, there is a MOUNTAIN of stuff written on here about front end shakes on Nissan Patrols from 80km/h to 110km/h mate, if there is not 10 different threads i reckon you will find 15 on this very subject.
Dont be surprised if the wobble gets limited with new tyres, if it does it will be because the tyres are absorbing the wobble till they scrub out. then they will be knackered.
Everything from rooted tyres, (you noted that they are due a change) (did it do it before? how long have you owned the car?)
To crappy panard rod bushes, loose wheel bearings, steering damper, Old knackered shocks, drag link or tie rod end worn?
All of the above should be checked BEFORE you give some wally your hard earned for a new set of rims. Nissan Alloy rims are tough mate, very unlikely to be your problem imho. Will be too bloody late when you lash out $1000+ for new rims to find the problem is there 6 months later when your tyres scrub out, bet they wont give you your cash back then.
After going through the ringer and a couple of sets of tyres i finally threw the book out with the wheel alignment settings from factory cause they are not set for the camber of Aussie roads.
I fitted a set of Offset King Pin bearings for the left front side to adjust the camber (not caster) by 1 to 1.5 degrees and did another wheel alignment.
PATROL - Safe T Steer
My GU IV now runs straight and true, no signs of scrubbing out, no side pull, no vibrations. One of the best mods i have done to my car.
Have a search mate.