Flat tire tip applies to your buddy with Mustang too, although if he has different tires front to back he might be screwed.
So you currently have a carrier in your different that looks like this (this one is actually 7.5" but was the better picture for what I'm describing).
At top right/bottom left are locations where the carrier bearings are pressed on. And they have to be seated correctly, so they don't shift after installation when you're applying power, but not forced so hard they are damage during installation, i.e. you need a press to install.
In the lower left of the center, you will note a hole which the side gear goes in.
View attachment 77841
There are 2 different side gears: On the left is the standard, on the right is the limited slip Left is actually from Ford 8", but the difference we are discussing is the exterior splines.
View attachment 77844
And the splines engage into the corresponding limited slip clutch plates
View attachment 77845
You will also note the tabs on the clutch plates which need a corresponding slot in carrier.
Limited slip carrier with bearings & side gears with clutches.
View attachment 77846
Between the bottom and top picture, you note the difference and why you can't just make your existing carrier limited slip.