I think your car is built like my wife's which has splined stubs sticking out from the front diff. The big axle cups are splined internally and slip over the stubs and are held in place by a spring pin. However, the stubs are held into the diff by a 'circlip' (w'ever) a circle of springwire in a groove. (IIRC)
Some of your initial symptoms seem to fit a scenario in which a 'hard' turn (to the lock) could have pulled on the stub enough to pop it loose - enough to compromise the diff seal - cause leakage of the fluid (which might blow back onto the exhaust) and maybe cause the smell (diff oil smells bad anyway - so it may smell different than engine oil if it got on hot exhaust) thuinking and other odd driveline sensations you report.
Doesn't mean any of that is correct, but it's something different to look for. (could be the previous owner got an axle that was too short - or, the stub was pulled out of it's groove just slightly when the old axle was pulled out, but your hard turn when reversing pulled it more, comprimised the seal, it bound-up and is now so far out of place is intermittently engaging internally)
I came across this in search and believe I have this happened. 99 legacy brighton wagon with automatic and 270,000 miles. Original cv axle. is not cracked. I have seepage from the drivers side diff, smell as it hits exhaust, and the clunking noise under load while accelerating even on straight line. not while turning. clunking got faster as speed increased. no clunking while still and engine running. If diff stub did "pop" out, how hard is it to get it re-seated?