I WAS wondering just how far out in the sticks you are.
It doesn't get anaerobic under the manure because it's so dry. Relying on natural precipitation leaves things fairly dry except for short periods of rain or snowmelt.
I think if you can mix some organic matter into the soil and then mulch fairly thick it will make it easier to grow things. If you can contour some areas to catch any rain or snowmelt it will help a lot.
