Peace' expresses covenant blessing in its fulness. Peace is wholeness, a harmonious abundance of everything promised by God. Peace includes, of course, peace with God, peace of mind, and peace in our relations with others. But it also includes material blessing and the opportunity to enjoy it. What we see here, by the way, is Christian culture.
Greetings are part of cultural life.
In most societies the words of greeting have had religious significance of some sort. It is natural for us to have greetings that differ from the world around us, for our greetings, like all of our lives, should express our faith in God and our desire to bring His blessing and grace on one another. It is unthinkable that a man with Paul's theological training would, by accident, seem to ascribe deity to Christ. He naturally assigns Christ a place of equality with the Father because it is the habit of his worship and praise. It is to the grace of the Triune God that we owe our salvation.