By chance does your car have a limited slip diff?

My experience with them on Corvettes is that as the clutches wear, axle yoke end play and differential gear backlash increase. This can cause "slop" in the drivetrain. It is especially noticeable when you start from a dead stop with a lot of steering lock and there is relative movement of the differential gears. Open differentials don't have the same problem since there is no clutch pack that wears noticeably with use.

You can qualitatively check for differential gear backlash, by having a helper hold one wheel while you wiggle the other wheel back and forth and "feel" for the play. More than about 1/16 turn play means the differential gear backlash is high. Note that "differential gear" backlash is not the same as ring and pinion backlash - two different gearsets. A lot of guys get them mixed up.

Duke