OK, I took a short nap and as often happens woke up with the solution. The
solution in this case is laughably trivial - if I turn the wrenches one way and
it removes the wrong shaft nut, the solution is simply to turn the wrenches the
other way. I have had a serious case of cranial rectumitis over this issue for
many years apparently.

Think if it were a piece of e.g. allthread. Grab one nut and put a wrench on the
other, and if you tighten one nut you tighten them both, right? Well, if one end
of a shaft has a RH thread and the other has a LH thread, then if you tighten
one you loosen the other. So removing isn't a problem, it's tightening that's a
problem, and that must be why everyone was telling me to use impact to tighten it.

Sigh. At least the world is back in order, and I got my other wheel off.

GWE