The limited slip additive works - because it makes the trans SLIP. But only if your problem is clutch shudder.

Plus it damages any brass materials - bushings and thrust washers.

And it reduces clutch capacity ( makes the clutch less able to carry the same load ).

If you haul a small trailer and back that van up a grade you'll wound the L/R clutch - guaranteed.

Before you use it - why don't you diagnose the problem more instead of crutching the situation.