FWIW:
Many of us have "looked" @ hyd oil and thought it looked great only to find milky chit/globby yuck in the rearend once the cover is pulled.
Start there first.
I'd use the inexpensive oil after clean up, then if you want to spring for the name brand stuff from Deere or IH, just knock yerself out.
Do not use the "303" tractor fluid, even tho' it is dirt cheap, it is really thicker than you should run, and causes problems in colder temps.