I have the same issue coming into my driveway. (And why I'll never be able to have a front splitter on my car.
)
I'm surprised that the LSD didn't lock up and push you through. Depending on angle/speed, my right rear tire often comes off the ground. I can hear the LSD motor zipping and get a clunk as it almost violently locks the diff up so I can maintain traction. Thought something was breaking the first few times I heard it. I try to avoid it though, as I can't imagine a hard slam lock like that is good for the diff clutch packs.
My son has an FRS, and the same issue for him. But that car has a Torsen diff, which handles this much better than a clutch type diff like we have.