Yes, I think that like Antony-Paul you pretty well nail this one down: Tradition and Scripture. Of course, the Anglicans add 'Reason' to that to make a trilogy, and one would hardly wish to be seen to e rejecting that!
Yet to let it predominate is, effectively, to make one's own perspective king. I have seen few arguments for women priests that did not convince me they were right - terms of this western world and its norms. But who died and made us normative for everyone else?
It is, of course, easy for HH Pope Shenouda to say what he does about women, as the society within which he lives has in it little mementum for the ordination of women; that does not negate what he says, but if we said it here it would, rightly, get the bum's rush from most women and many men. Indeed, it can be difficult importing some of his arguments into the West. I was once upbraided by an Anglican friend who quoted some remarks from HH Pope Shenouda on the subject of homosexuals which, I have to admit, would have had him having his collar felt by the old Bill had they been made in the British press. Egyptian society operates on norms which our own has long abandoned.
But if we rest where you advise, Scripture and Tradition, then in the case of both this subject, and the other one, we have reasoned arguments to suggest that the employment of Western norms alone is not a reasonable solution to the perplexity.
In this is love, not that we loved God, but that He loved us and sent His Son to be the propitiation for our sins. (1 John 4:10)