Craig

Mark said

It still raises the question I asked you earlier in this context. There is a parallel here between husbands and the Lord. If the submission to Christ that the Church offers is without authority then it is for wives to husbands.

Yes, because submission to one another has to also be in the mix, and it is difficult to see authority there. Perhaps the word authority isn’t there because it is not essential to the meaning of the word submit and Paul is concerned about encouraging submission and not authority.

Mark said

And so my question to you is – do we sometimes submit to Christ in an authority-kinda-way but we don’t other times in the NT? And if so, how do we work out which submit is on view in which text? Or do we never submit to Christ in an authority-kinda-way, submission to Christ, God, ruling authorities et al just does not have any authority connotations in the NT?

I’m not sure that I fully understand your questions but I will have a go.
I think it is possible to submit to Christ for various reasons- some of them good and others not. I may submit to Christ because He is my King and my Lord and he commands me to submit to Him because of His authority. I think this is appropriate because He is Lord of the universe.
If the NT says for me to submit to Christ because he is my Saviour who loves me and gave his life for me it results in the same action (submission) but for a different reason, and I don’t think authority is what it is about. I think it is possible to submit in a Galatians error legalistic-kinda-way. It is also possible to submit to Christ in a John 15:9-17 “you are no longer my servants but my friends whom I love” kinda-way.
We can respond to Christ in submission out of respect for his authority or out of love and thankfulness for all he has done for us. Both are valid. Ephesians 5, and the head-body metaphor seem to me to be emphasising the latter.