lol, c'mon now, lets pretend that i may have been around a few cars in my life.
having said that, first i gotta ask about the bolded statement. when you say "lifts up" are you saying that it literally lifts the inside rear tire off the ground? if so, i would be REALLY interested in seeing some examples of solid axle cars lifting the inside rear tire. i can find plenty of examples of IRS cars lifting the inside rear tire - mainly FWD race cars with full cages and REALLY stiff rear sway bars.
second, i have to disagree with you about how one tire affects the other on a solid axle(a 3 link, 4 link, torque arm, or similar solid axle suspensions anyways). one tire lifting over a bump or drooping into a dip doesn't cause the other tire to do the opposite. the other tire simply maintains its current position along the Z-axis, so long as it doesn't encounter a bump or dip of its own(though its contact patch is obviously affected by the opposite tire as it moves along the Z-axis). now, a single pivot tractor axle will act the way you described...
...but that's simply because it's designed to pivot around a central axis, while the 3 link w/ panhard on an S197 mustang isn't.
finally, what does this have to do with the aforementioned "monocoque problem/effect" and how an X-brace in the rear bulkhead fixes this?