you seem to have jumped in Philippians 2:6 to seeing Caesar not Jesus as its primary referent…

I don’t think so. Jesus is the primary referent, but he is portrayed as the one who does not do what Caesar has done, which is violently, arrogantly, to seize equality with God.

I agree with your later statement:

Or maybe the idea is that if Jesus had not been prepared to give up his rights, he would have merited the criticism which ‘grasp’, or ‘seize hold of’ conveys, and would have demonstrated the abuse of power, or lack of servant heart and self-denial which lie at the heart of an anti-christ attitude to power.

Perhaps a few people could pray for Peter…