That second picture is a big help. You won't have any problems with the lower section of the slope...it'll just be the section abreast that deck.
So, mow the lower section pretty much however you want to (going across may be intimidating since the ground appears to be a bit rough) and back up the 20 feet or so of that upper slope. That looks quite a bit like the section I'd described in m first post in this thread (except in my case, there's very little level at the bottom due to the tree line).
The transition between the lower and upper section is pretty acute. I don't think you'll be able to use a solid upper link on your 3PH. That does complicate things a bit. The problem is, if your cutter has a rear pivot wheel (as most do), it may try to go sideways on you while you're backing up the slope. So, slow is the speed and if it gets squirrelly, stop and go forward. Even if you cannot get it all, at least there'll be less to weed wack or do manually.
So, I suggest you give it a try, but don't be a hero. If it feels unsteady, don't mow it with your tractor/cutter.
If you go with ground cover, consider juniper. That stuff is pretty, very thick (almost an evergreen in appearance) and inhibits weeds (once it takes hold...might take a year or so, depending on how closely you plant them). Here's some info:
Blue Rug Juniper for ground cover