yet another gear oil question

The Motorcraft fluid does not come with Friction Modifier even.

Do not use cheap fluids, if you cannot afford to do it right wait until you can.

AFIK only RP comes with the friciton modifier in it and I would not use RP in my lawn mower.

You should be able to use conventional 80W90 gear oil. The newer cars require the 75W140 synthetic. There should be a tag on the diff that says for sure or refer to the owner's manual.