This goes hand-in-hand with a point I was trying to make a few threads back - lotsa guys figure if their LS doesn't chatter after a lube switch, they're home free - overlooking the fact that just maybe they no longer have an active LS because the new lube is TOO slippery...
If I were you, I'd drain and refill with a standard dino lube with NO additive, and run it for a while that way - allowing enough time for the new lube to fully coat and penetrate the differential clutch material and return to normal operation - if at some future point the LS begins to chatter, THEN you can add additive - but it might take a while to reach that point, so be patient...