Unfortunately, the schism (or whatever you wish to call it) in the Alexandrine See actually pre-dates the antipopes of Western Europe by several centuries.
The split over the definitions of the Council of Chalcedon - and, I believe, the political factors involved - generated the two claimants to the see of St. Mark which persists to this day.
As to who would step down if union were achieved ... well, you'd have to ask the enthroned ones about that!
(As you may have noticed, there is a similar situation in North America today, where the unity of the Holy Confessor St. Tikhon's day - within the past century - has given way to numerous overlapping "jurisdictions" of bishops and Synods. Since this is against the canons of the Church, perhaps they are all "uncanonical", in a sense.
Still, "History Happens", and the Lord is Compassionate and Merciful...
In the current situation in both cases (America and Alexandria), it is perhaps not unlike the many confusions which the Church has undergone in all Her life. Even in the midst thereof, "the wind bloweth where it listeth".
I like your icon of St. Rafka; I only recently learned about this Maronite Saint.
Such true Holy Ones perhaps show, through the love and ascetic labours of their lives, that God's presence and call is, and always will be, to all nations and peoples!
Holy Flower of Lebanon, St. Rafka, pray for us!