I ended up with an old Toro Groundsmaster Batwing. I don't think it would be possible to roll it over on a hill. However, it struggles with enough power for driving uphill. It is 4x4, but that isn't enough.
I've been meaning to fix up an old mini-dozer with a 3PT and PTO to try mowing. Yet, my hillside is steep enough that I need to figure out how to put on a ROPS. It is hard to imagine rolling the dozer, but there must be a reason why they put the ROPS on the newer ones.
If it is within your budget, there are quite a few tracked skid steers that would make sweet mowers, but it could be a significant investment.