Origin does not negate "co-eternalness". The Hypostasis of the Trinity "is" before time came into being. Origin from the Father, however, is important lest Christians fall into any of a number of heresies; Arianism, Nestorianism, Macedonianism, Modalism (especially)...there are others.
"If it is purely extra-scriptural then we may well ascribe different meanings to the Creed we jointly recite."
You are of course free to believe what you will. The days of the Inquisition are over. The Church, however, has never had multiple "meanings" for The Creed, aside from the West unilaterally changing The Creed by inserting the filioque, which did change the meaning and was correctly anathemized by the East.
"Creeds are only human summaries of what I consider authoritative, they don't have authority on their own."
Because the Nicene Creed was adopted as a dogmatic statement of our Trinitarian Faith, it does indeed have authority on its own, at least within The Church.
Should be "Hypostasia" not "Hypostasis". Sorry! You all might find this article on the Trinity as seen by +John Chrysostomos interesting. It is thoroughly Orthodox Christian.