http://www.mustangsteve.com/msFAQsuspension.html
My technique to remove the big nuts...  Place the 1-1/4" hex nut in your securely mounted vise on the workbench, with the shaft sticking straight up.  Then get a long pry bar (piece of pipe) and stick it through the control arm and use it as a big lever to rotate the control arm to loosen the shaft.  Notice the pry bar in Deb's hand, getting ready to remove the second nut on that control arm in the picture.



 

Put them back together and weld the  nuts on per my web page.  it actually does you a favor if the threads are stripped because then you can position them where they do not bind on the threads.

The fine threads are actually a double lead thread.  There are two sets of threads, side by side, so the helix is the same as the coarse threads on the shaft.  That way they thread together at the same rate on the coarse threads AND the fine threads.  Stripped out works fine if you tack weld them. 

The ones that have good threads and you cannot rotate the shaft in the nuts when you reassemble them are the ones you will hear squeaking, even with grease in them.  The nuts bind up and try to tighten like a bolt clamping two parts together.  But a bolt doesn't have to rotate.  If they are in a bind, rapid wear will result.  Stripped threads let you rotate them for best fit before welding.