This is totally ghetto, but adding molydisulfied to the oil in your diff will cause the clutches to grab better. (Sounds wrong, but I think the moly particles build up between the plates, so the clearances change, and the clutches then engage better.)
Ran the moly additive in my MK2 for years to help with, and mostly cure the rear end whine/howl that had developed, and it also made the LSD work again... Burnouts with both tires spinning, not easy to do on the NA160hp 5M engine, but possible. When I added the same stuff to my MK3 LSD, it made it so tight it would chatter, pop and make horrible noises at any low speed when turning. (Too tight short of a race car.) I had to wash it out with two cans of brake cleaner, and it still was pretty tight. (Is tight I should say.)
Hit up a parts store, something more Mom and Pop vs Pepboys, and it's generally near the Lucas stuff. (Ask for moly additive for gear oil.)
Besides, the moly is a great high pressure lubricant, so you get the best of both worlds, less gear noise, better lubrication, and a tight diff. (Clutch type I suppose it the only one that would be affected, if it's a Torsen, no change should happen.)