Am I a weird naturalist?
My concept of the natural happens to exclude God, since on the working definition that I operate from, teleological and intentional explanations are basic explanations. But God has a character, a nature, and if we knew enough about that character we would be able to predict God's actions. To some extent people are able to predict the actions of God. So if that makes God natural by your definition, I have no trouble with God being natural, or even, for that matter, God being physical.
In defining the physical, my dissertation advisor Hugh Chandler once, in class said that physics is whatever physics quantifies over, and some theories quantify over God, therefore if those theories are true, then God is physical.
Biology is the science of living things, theology is the science of God. Gosh, maybe I'm a naturalist after all. Just a weird one.