LSD would have kept power going to both rear wheels. You probably wouldn't have gotten stuck. Four wheel drive is even harder to get stuck. However, if you do manage to get one stuck, then it tends to be really stuck and harder to get out. Tracked vehicles have ridiculous traction, but when you get one of those stuck (and I know people who've done it), getting it unstuck is quite a project.

My personal best stuck was with an International Paystar 5000 6x6 tractor pulling a 32 cubic meter end dump full of gravel. At some combat outpost I never heard the name of in Al Anbar, I bogged down in some deep loose gravel. They hooked up two MTVR's (7-Ton in USMC-speak) to try to pull me out and I managed to break the jackshaft between the transmission and transfer case trying to power out of the gravel. Then they went and got a D7G dozer which pulled me out no problem. Luckily our support truck had a spare jackshaft which I changed while the rest of the team went back out for another load. Upon return, one of my friends got his Paystar stuck and was pulled out by an Abrams tank. I managed to get a picture of that.

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Whoever said there's nothing more expensive than a cheap Mercedes never had a cheap Jaguar.

83 300D Turbo with manual conversion, early W126 vented front rotors and H4 headlights 401,xxx miles
08 Suzuki GSX-R600 M4 Slip-on 26,xxx miles
88 Jaguar XJS V12 94,xxx miles. Work in progress.
99 Mazda Miata 183,xxx miles.