OP, this will be a long ramble, but maybe it will make sense at the end.
I mow up to 20 degree slope with my CUT. It's heavy, and rears are filled (over 7k pounds with mower on). Mowing with a 6ft brush hog on back. 20 degrees is about all I want, and the pucker factor is right up there, at least for me. The worst slope area, I will mow vertically, as in not trying to side hill that spot, which with it's variations in hillside, has a few spots that go over 22 degrees. Unfortunately, that spot, is right above a rather large concrete culvert, that if I were to lose traction there, would be about a 6-8' vertical drop to the bottom of the concrete culvert.
With my CUT in 4x4, low range, and rear diff lock engaged, I can pull vertically up the sides of the culvert (steepest part of my hill is right around this culvert), mowing upwards as I go. Then I either drive around the slope and make another pass the same way, or for the slightly lessor angles, I'll back back down that slope again to pull up another pass.
Doing it this way "works", but I'm not a fan. The ground has to be bone-dry. No dew on the grass, and no moisture on the slope. If we weren't moving to a new location in the very near future, I'd probably look at some other method to mow this slope area. I do want to keep it mowed, as it's right along a very busy local road (county hwy), and the local brain dead's are constantly tossing garbage and cigarette butts from their cars, and I worry about grass fires in the summer dry seasons, which up here, can get very dangerous, very quickly.
If I could just let it go and NOT mow it at all, I probably would. The CUT does work, but it is a bit gut-wrenching in a few spots (like backing down over the culvert at 22 degrees, and staring out the back window at the bottom of that culvert, LOL!). The "nasty" parts of my slopes are maybe a couple hundred feet long. The rest is low angle enough to not really be any concern.
If you only have one small spot that the slope makes a 19 degree max angle, I think a SCUT or CUT with 4x4, diff lock and filled tires would work, even if you have to vertically climb the worst part of it. It won't be "great", but it works. If you have a long section of slope that goes 20 degrees plus, then maybe you will have to bite the bullet and go specialty mower.