OP's problem sounds like me last fall trying to get the trailer out of the yard for the trip to Florida.
4x2 with limited slip. Heavy trailer (8000#) lots of tongue weight (1200#) and All-Season tires.
Wet grass, saturated soil.
When both wheels start spinning, the limited slip isn't going to help much. All I could do was turn off traction control and rock it out, slowly, with several stops for throwing sand/gravel under the tires. Perhaps wrapping rope around the tires would have helped.
Since then I've put a load of gravel down. But still, the next truck will be a 4x4 with All-Terrains. Then I can really get her stuck!:B
