Those slopes do not look too bad at all. I use my JD-L111 with turf's on the back side of the slope. The JD with the B&S twin does fine although the one thing I do not like is the turfs. Would much prefer the AG's but I won't go to those simply for the pond. The front side (pond side) of the hill I do not mow at all yet and will not until I can get a sickle bar mower either a 105 balanced head for my Cubs or similar for the CC, I prefer though my old Craftsman Gear Drive for doing the slopes. Even though it may be the least desirable, it has been the most dependable for me and I have mowed the slopes for years with it. It is the one rider that I have never worried about rolling over. The biggest problem with a Gear Drive for me has always been reverse... that is really scary. Both puker factor events I experienced were on that gear drive - one rolling backward into the pond and the second rear flip when loading on a trailer.
You should be able to handle your slopes with the 1200 but keep in mind it's limitations. If you can add the ag's that would be super and make it less prone to slip.