this works just fine. The slanted roof shunts the smoke out into the open and keeps the rain off the fire. The hearth is surrounded by the rock walls here, you can't see it but its just a ] shaped wall around the hearth that blends with the oven exterior.
https://steamcommunity.com/sharedfiles/filedetails/?id=2924987564


from the other side:
https://steamcommunity.com/sharedfiles/filedetails/?id=2924987771

I personally put fires on my topmost story if possible, to avoid making a slice through the home. Time its said and done for oven and just 1 hearth (and I often have 2) its too much space, and then there is the tub...