Well, I'm camped at Gum Woolshed, the shearing shed at Pernatty Station in the Northern Pastoral District of South Australia and discovered a flat tire on the ute. Obviously it's gone down overnight and I'm really glad it happened the way it did because it would have been a major task had it been on the highway.
So with the tire pumped up to give more height for the jack, I got the wheel off, though one of the nuts gave considerable difficulty. The thread picked up and partly stripped. Not good in the outback.
I figured if I could find the puncture, I'd fix it myself with a plug that I have for emergencies on the quadbike tyres, but alas, even with a dish of soapy water I couldn't find the puncture.
More importantly, the question of what to do about the damaged wheel stud and nut. Run with five nuts instead of six?
After several unsuccessful attempts at fixing the damage with a small file, I scrounged around the junk surrounding the old roo chiller (that's a cool-room once used by the kangaroo shooter). There used to be an old Landcruiser here, a roo shooting vehicle. Two Landcruiser diffs are on drums nearby. No sign of wheel nuts. I went through all the boxes of parts and junk searching for a Landcruiser wheel nut with the expectation it would be a different thread if I should find one.
When all hope had about gone my eyes fell on a nut on the ground among the junk. A clean up of the thread by winding it onto one of the Landcruiser wheel studs and I was ready for the big test. A bit of filing of the damaged part of the thread on my wheel stud and with some patience the Landcruiser wheel nut screwed on; the right thread after all!
So it's all OK. Both rear tires are well worn. Looks like two new tires when I reach either Roxby Downs or Port Augusta. In the mean time, I still have a spare tire since I travel the outback with two spares.