For my part, I think the most interesting way to think about orthodox Christology--fully God, fully human--has to deal with divine Being and creaturely being.
Specifically, as many theologians have pointed out, ancient and modern, the Incarnation is only a paradox if divine Being and creaturely being exist in the same ontological space. But if divine Being is different from creaturely being, then no ontological jostling occurs. God and human being don't become bumper cars, banging into each other. It is God's ontological difference from the world that allows for God's non-competitive relation to the world. Here's how Robert Barron in his book The Priority of Christ describes it:
If in Jesus divine and human nature come together non-competitively in ontological unity, there must be something altogether different about the divine nature. The divine way of being must not be a worldly nature, one type of creaturely being among many; rather, it must be somehow else. The difference between divinity and creatureliness must be a noncontrastive difference, unlike that which obtains between finite things. God is indeed other than any worldly nature, but he is, if I can put it this way, otherly other. Nicholas of Cusa expressed this paradox neatly when he said that God is both totaliter aliter (totally other) and the Non-Aliud (the non-other).
Even further, the implication of the non-competitive, non-contrastive relation that we see in the the life of Jesus becomes a possibility for human existence:
The proximity of God is not a threat to a creature, but on the contrary, that which allows the creature to be most fully itself. If a fellow creature were to enter into the very constitution of my being, I would be the victim of aggression, and my freedom and integrity would be undermined. But the true God can enter into the most intimate ontological unity with a creature, and the result is not diminution but enhancement of creaturely being. God and the worldly are therefore capable of an ontological coinherence, a being-in-the-other, so that each can let the other be even as they enter into the closest contact.
