Excellent treatise on the subject. I would, however, like to add my emphasis on "Emmanuel", that instead of simply 'God with us' as in the mere spiritual sense, it would be better interpreted as 'the one who walks among us, is God'. Giving more clarity to the incarnation of the second person of the Trinity.
In Eden, God walked with Adam (and Eve); see Genesis 2&3
After they sinned, He drove them out of the Garden, and walked with them no more.
When Jesus was born, God walked the earth with Man once again ...
John 1:
11 He came unto his own, and his own received him not. 12 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
This time, though, when He left He sent His Holy Spirit to teach us all things.