Except its going to be impossible to make things flat/level/smooth due to the other rocks sticking up all around where you are trying to cut down in...could maybe cut some chunks out with a diamond blade and then level/smooth things out with a diamond cup...personally, I really think I'd just grout some little steel platforms for the legs to sit on, or do the same thing with a stove size steel plate...
His stove (looks like a heritage) has 4 skinny feet that only need 4 little flat spots at a specific place at the same elevation. The rest of the hearth can be a cobble mess.