Some thoughts on posts on this thread:
1. TRUE slopes of 25 and 30 degrees may be considered "climbable" but they are not walkable, and certainly walk behind self powered equipment needs assistance in working on such sloping TRUE 25 and 30 degree slopes (in other words you either have to help with traction in pushing or in considerable effort keeping the mower straight. And these opinions are made under normal grass/turf conditions and heights. 10 inch grass is not normal - nor does it allow for the same level of traction or footing as normal turf smoothness. "Can you walk behind" cut 25 and 30 degree slopes - depends on how far afield you want to define the word "safely".
2. For many years I've cut TRUE 20 and 30 degree slopes - both when the land was undeveloped - and when it was fully developed. Going downhill in a walk behind situation is as dangerous as going uphill but for different reasons. In my opinion it is not reasonable in any manner - to assume a walk behind is a safe, consistent, and convenient long term solution unless the length of that slope (up and down) is less than 25 feet or so - and that goes for 30 years old or 60 years old.
3. There are many slopes and sidehill slopes that are safer and easier to do with a quality mower or sub-compact tractor compared to a walk behind and when you are describing 10 inch grass and non-level ground - its even more true. But I wouldn't try the same slopes or sidehill slopes with a compact tractor - that I would with a sub compact - because a sub-compact is closer to the ground - as is the driver. Those 2 items being closer to the ground means a lower center of gravity and a resulting better traction (assuming proper turf oriented tires).
4. Besides products like the Dixie Chopper XCaliber 4 x 4 - there are also some unique ground care mowers like the Toro ride-behind zero turn "stand up" units, or the Cub Cadet I series I1050 zero turn tractor (that I also have). Each of these units is also low slung and low center of gravity and designed for slopes.
My point is - if you have TRUE 25 and 30 degree slopes you aren't near as cocky in cutting them - because each and every time you do it - you know you can't be careless or "casual" about it. Many friends have looked at my slopes and thought they were 40+ degree slopes - because recognizing actual steepness is something for slope levels - not visual for most people. And 60 to 80 foot long slopes is a much different story for regular mowing also than 250 foot lengths.
I'm not a know-it-all on slopes - but I've had my share of slips and "almost lost the mower or a foot" or watched 25 year olds struggle carrying a bucket of something on a steep slope, to know today's traction is always changing. My Massey sub compact with turfs and my Cub Cadet I1050 both cut very well and very safely on steep slopes and sidehill situations without hurting the turf - but its NEVER an "automatic" process or a "phone it in" performance. My goal is to live longer than my equipment and with all my implements properly attached LOL.
By the way in case you are wondering - no - I don't cut with the fel and bucket on