Yikes.. grey tranny oil is bad.. that means it is very water contaminated. If it were mine.. I'd buy a can of seafoam transtune.. add it.. run it a few minutes, then change the oil using cheap as you can find walmart supertech oil.. ( 17-18$ for 5g ).. then drain after running it around the yard for 15-20 minutes... then I'd drain it again, and change the filter. By the way.. nothing wrong with that cheap UTF. My tractors have been getting walmart and TSC utf for years.. no issues.
The extra oil change may cost you another 20-30$.. but it is cheaper than replacing the hydro pump, and tranny bearings...
Soundguy