valvoline does not come with the friction modifier! call them and talk to an actual engineer.
the modifier is there from the factory to make vehicles more street friendly - cater to the average Joe who doesn't ever wheel a jeep. you can buy a tube of it . some auto places even actual carry it.
clutch packs in a LSD die over time. Kevin, in your example, its from beating the snot out of your rig, not the fact that you did not add the modifier, which was NOT in the valvoline you bought.
I would not run it in a vehicle you wish to offroad .
I also would not plan to run a factory LSD for too long, even rebuilding the clutch packs and adding more clutches wont do much.
The LSD additive is not needed.
I have been Not running LSD additive in every LSD diff I have owned over the last 15 years, I have broke a lot of crap, but not a LSD. Also, don't forget , that LSD in your 44 is probably almost 30 years old, so rebuild the clutches, and then run no LSD additive. Best choice is to get rid of the LSD carrier and swap in a detroit/grizzly.