Perhaps a more modern day image is that of an email attachment and its relationship to the email itself. The Blessed Virgin is not like the email to which God has attached something -- separate and distinct from the Virgin, drawing nothing from her and her flesh and blood but only sent with her and through her. In the same way, the bread is not the email to which God has attached His Body but the two are separate and distinct (see disclaimer below)-- only only the agent of the sending and the other what is being sent.
Keep writing great posts, Fr. Peters!
Disclaimer: With regards to the Orthodox understanding of the bread and wine and their relation to the body and blood, we do not regard the two as separate but having undergone a change. The priest (NOT the congregation) beseech the Holy Spirit to make these things the body and blood of our Lord in the epiclesis. We do not understand the nature of such a change, hence we do not subscribe to transubstantiation as the Roman Church does by chanting the verba but we know that change has occurred. How this is accomplished and when, we do not know but are content to leave it a mystery. Nevertheless, we confess that we receive the body and blood of Christ. My apologies if I seemed to endorse a non-Orthodox teaching.