Dear Simon,
Yes, you correctly described the early church position. There seems to be an essential unity of thought regarding the headcovering, men teaching and leading, marital headship, etc. If you would like to read the references for yourself, I’d highly recommend David Bercot’s “Dictionary of Early Christian Beliefs” which has compiled the direct quotes from the early church on this subject and many more. I’ve benefitted very much from that book as a springboard for research.
