Better yet, grade the slope up with some rich mix top soil and 10% compost. Take the steepness out of the slope. It will at least minimize the slope making it safer on a mower. Good chance to level the yard out too.
I've been mowing 2 acres of 20 degree slope for over 5 years with an RTZ-SX54. Both the Kawasaki engine and frame are rated for this. No problems running across or up/down. Starting to think about replacing the RTZ. Will definitely be one of the steerable CCs.