I used to mow a property a couple years ago that had a slope that was a ditch against a state highway and with a 54 inch deck it was 5 full passes on the sloped side by the highway. The top pass was probably 30 degrees and the center 3 passes were pretty close to 40 degrees if not just over. The bottom pass was about 30 degrees also. That's just a guess off the picture of degrees that was posted. I know it was steep enough that the variety of mowers I had over the 15 years I mowed it I had a pretty good idea what I felt comfortable with. I would suggest a mower with diff lock, I mowed that slope with cub 129, JD gt235, JD 318, JD 425, JD 455, and a JD 757 ztr. The 425 and 455 worked best because they have a wider stance and diff lock. I would say in my list in choice would go 455, 425, 318, gt235, 757, 129. The individual brakes on the 318 was nice but on the 318, gt235 and 129 when the back wheel would lift just enough the topside tire could spin and then you were stuck on a steep hill. I only mowed the hill horizontally because if it was wet I couldn't make it up the hill and I would have to drive to the bottom and down the other side then mow it all one way. The 425 and 455 could climb the hill. A 345 or gx345 was replaced by the x540 and they have diff lock, the early model 345 didn't have diff lock. If your topside tire lost traction the diff lock would keep it moving atleast.
When I mowed that ditch I had to sit atleast one cheek off the side of the seat towards the top of the hill, otherwise I would be up on 3 wheels. If your tire does start to spin and you don't have diff lock, if you still have momentum you can turn down the hill. Otherwise you back down the hill and that is a bad feeling and when the ditch had some water in the bottom of it you could get wet in a hurry.
That 757 was a sled when it was damp at all, but when it was dry that thing was extremely stabil.
Just my thoughts from some experience. I wish I would of kept mowing it since I have a JD x585 with a 62 in deck and the 4wd would be awesome on that hill.