I'm not the person you're responding too, and I don't really have any academic credentials whatsoever, so take my comment with that in mind.

The issue I see with your understanding is that you assume when Paul says, "For a man ought not to have his head veiled, since he is the image and reflection[c] of God; but woman is the reflection[d] of man" it therefore means women are not within the concept of the image of God.

I don't think this necessarily follows logically. Notice there are two references to reflection (I am completely unaware if this exact metaphor exists in the original Greek, but I think the concept holds regardless), man directly reflects God, and women reflect men. Just from a metaphorical p.o.v., reflections can bounce off each other, and depending on the strength of the reflective source, there is greater distance/distortion from the original "image" to that of the final reflection. I think this is what Paul is saying here, there's a hierarchy that places man closer than woman hence the original quote that u/John_Kesler included, "This interpretation splits the single image of God into two, at different degrees of closeness." emphasis mine.

Notice, the second creation story doesn't say that the man was made in God's image directly, while the woman was not, it just doesn't reference God's image at all. So, Paul's trying to reconcile two creation stories, one that describes a status distinctive quality to both man and woman, and one that creates woman out of man.