Hi Turf Man,
A JD 335 zero turn has never been good on inclines unless going straight up and down, even then they get a little unstable.
Years ago, I recall as a kid, I watched my grandmother mow steep inclines with a basic, light small push mower that had a rope tied to the handle. She would stand at the top and ease it down the incline, then move over a foot and pull the mower with the rope back up, it worked pretty slick.
Also, I agree with hlw49 about the CC steering wheel design zero turn mowers; they hold the ground much better and are easy to control going across inclines. (I own an RZT S50.) A trick that helps is to place a 50lb weight on the front so they can maintain directional control much better.
When it comes to most zero turns, weight distribution is a critical factor, most are designed for use on mostly flat ground, when they hit inclines sideways, they tend to "crab" and slip as they travel forward.
Another mower that also works great is an older Snapper Series 6 rear engine rider. They were (and still are) a workhorse for changing inclines, but a front weight was also recommended on them as well.