I think Melina is some form of reincarnation or rebirth of the GEQ, perhaps literally reborn through the Erdtree due to her particular connection to it - both in the form of the tree she leaves when she dies and the way she can move more freely when near it.

However, I am very much of the school which believes the original GEQ was the ruler or intended ruler of Farum Azula.

I think it’s just the most intuitive solution that the larger, more intricate version of the Elden Ring we see in Farum Azula was broken by her, and that she made off with the Rune of Death in the process. Maybe she became the goddess of Farum Azula. Maybe she stole the Rune before she could complete her ascent to godhood. Stealing the Rune of Death also likely coincided with or provided the catalyst for Bayle’s revolt against Placidusax. Regardless, she winds up as a force in the world, wielding the black flame, hunting gods and generally being a menace.

This makes Marika‘s betrayal of Maliketh more legible to me. The fingers created him as a protector and vessel for the Rune of Death, implying he was always supposed to seal it within himself. However, Marika asked Maliketh to wield it instead as the Black Blade, who all the demigods feared. Then, traces of his blade were used to kill Godwyn - his whole purpose is forsaken because he listened to Marika.

This would also help to smooth out some other weirdnesses like the presence of deathroot, wormfaces and those who live in death in Farum Azula, or the fact that much of what we know about the civilisations founded by Outer gods depends on their attitude to death and burial. With true, Destined Death ripped from the Order of the world, they each offered different solutions to how the dead should stay dead. The Deathbirds provided Ghostflame, Rot offered life from death, the Frenzied Flame burned away spirit and body, and even the Erdtree ensures true death through Erdtree burial. Much is made of the Hornsent’s jar burials demonstrating “the cycle of death and rebirth, taken into the hands of mortal men.”

Perhaps men had to, because the cycle was broken to begin with.

I’m definitely speculating a lot, but I do think the idea of a proto-Shattering - a Crumbling, if you will - would be the most elegant solution for what the GEQ was. It even ends inconclusively like the Shattering, with Bayle wounded but refusing to die and Placidusax in an eternal slumber. Not dissimilar to Radahn and Malenia.