First I live on a hill too. My front yard in the steep parts is 22*, more in parts.
For your digging, rent a mini ex. They are way faster, stronger diggers anyways, let alone more sure footed.
You could mow what your slopes with a BX in 4wd. On the steepest parts you have to be very careful to not get side hill with an elevated load when using the loader. Straight up and down is OK. You should load your rear tires too.
The Ventrac as suggested would handle those slopes with ease in any direction, problem is it has a very limited loader. But as a slope mower it would stick like glue. There are lots of online vids.