Before we were married, my wife had a yard service that used a zero turn ride on for most of the lawn and a hydrostatic walk behind for her steep hill, which may or may not be as steep as yours but seems many times wider. I bought a used one with a Velke/sulky (less than she paid the service annually) for the whole acre lot and alternately cut the hill at an angle as described previously. The mower works fine but the Velke would slide on the steepest hill if I cut horizontally so I just hung it up on the hook the prior owner installed when mowing there. Walking slightly downhill of the mower allows you to be more upright.
A self-propelled push mower works, but this is wider, faster, and much more stable.
Our current home is on the side of a hill with a third acre of 150 feet of up and down mowing a 30 percent slope. At the bottom is a 3 foot drop off (flood plain change) and heavy woods. Riding anything that could fail would be risky, even my tractor or ride on with seat belts and roll over protection.
BTW, I am handicapped, have balance issues, and need at least one cane to walk safely.
The perennial flowers sound great, except they don't last long. Ground covers seem to take forever to spread and still have weeds growing within, often unsightly large ones. Wildflowers are often annuals and have the same issues.
Is there somewhere you can rent a walk behind to try one out? It looks like you might get by mowing the whole bank horizontally in two or three passes. Up and down on that small a slope would take many times longer.