This noise is absolutely the limited slip diff. It's a cone type diff. These can be noisy turned tight, especially after fluid changes. There is wear wherever there is noise, however, many have run thousands of miles with the noise and no ill effects.
Friction modifier will not be recommended by the manufacturer because of risk to the blocker rings in the trans from its use. That said, I added a touch of it after MT-90 because I couldn't stand the racket from the lsd and I've had no issues. You can buy a small bottle of FM at any Ford dealer for a couple bucks.