Geeze,
I hate computers. I just posted (I think) and yet it is not here. One more try. Please excuse stutters.
Russian River - not too cold in winter? Mid-20s at the lowest? Steelhead swimming and frolicking?
oops - different forum.
I'm thinking it sounds pretty easy. First check with your local building dept. to make sure you don't need a permit. Find out the recommended depth for footings for your area and soils. A French drain or other drainage system that surrounds the perimeter at or below the depth of the footings should keep your oven safe from frost heave an erosion due to your drainage situation. Again, the building department can recommend the best solution for your site.
Otherwise, it sounds like a standard build with a bit more backhoe or shovel work involved to remove some of the hillside.
I'll shut up now and let the more-informed speak. Hope that helps. Do I get some free oak firewood?