Yesterday I took the SJ to the Tyre Centre and got all 4 wheels balanced. I chose to do all four so I can mix and match the wheels around the car without worrying about balancing.
With the wheels balanced the drive home was much better, but not perfect.
The "wobble" we are getting is not a death wobble, its more of a mechanical vibration. Our SJ has fixed hubs on the front. This means the front halfshafts, CV joints, Differential and front propshaft with its UJs are all rotating all the time, even when in 2wd.
The next stage is to "eliminate" this from being the possible issue. By removing the fixed hub (see picture) it stops the wheel driving all the parts at the front. I have manual hubs on BigJImny so I will put them on the SJ and see if disconnecting everything cures the issue.
I am pretty confident that this will work as the vibration is very similar to what you get on BigJimny when driving in 2wd but with the hubs locked.