Like I said, I bought Acura trans fluid from Acura. As far as I can recall, the price was about the same as anywhere else except maybe Walmart or the dollar store. Tie yourself in knots trying to save $10 on a fluid change.
You just go to the parts counter and ask for the number of quarts you want. No phone calls needed or chemical analysis or anything else. They usually are pretty friendly and free coffee in the lobby.
Not related to OP’s problem, but as way of an explanation, posi- & limited slip differentials use a set of clutch discs to prevent all the power shifting to just one wheel. Hold your hands together and twist one CW and the other CCW, that’s how it works. If the discs are sticking too much, chatter while turning. If the discs are lubed so well they don’t stick at all, differential works ok, but lacks the positive traction function, so all the power will go to one wheel if the other loses traction. The lube additive makes it more slippery, and is used to achieve the best compromise.