I think that the main issue for the bottom category is the brain rather than the body. I wouldn't call it the self, that is too broad, the self is all three together.I am not exactly sure about your categories. I might be tempted to employ the spirit, the soul, and the self. (Although there is something to be said for the "body" in regards to incarnation theology.)
These are not separate enough, when the lover and the beloved are the self there is not multiple persons.That being said, I believe that the defining characteristic of God is that "God is love." (1 John 4:8) And "love" is a triadic relationship in which the lover and the beloved are united as one in love. IOW, God is both the "lover" and the "beloved" because God is "love" itself; this is the Trinity because these three (i.e. the lover, the beloved, and love itself) are one.
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