While I know for sure that the Chevron "Synthetic All-Weather THF" meets the JD spec for this and several other TT transaxles, I would stick with the Low Vis HyGard. I'm a long time JD tractor owner and have always used HyGard where indicated, with absolutely no complaints. The fact that it is very reasonably priced, makes it a no brainer. I wouldn't be surprised to find out that Chevron makes the HyGard, but it would take some searching to get that info. JD has a lot at stake in what they recommend, and I'm confident they wouldn't recommend anything but the best for their transaxles.
I know it's a natural tendency to want to "change", "imporve", "re-engineer", or "second guess" the engineers at the factory, but don't change what is known to work, not to mention recommended by the guys who build them.