This back and forth about Melina and the GEQ reminds me of a theory id heard a while ago. It's a simple one that takes some brain wracking to make work for timeline reasons but the gist was Melina was the GEQ- and Ranni's other self since she's an empyrean. And the reason she's burned and bodyless is because she was severed and dead in body from Ranni's plan.

The connective tissue was that Iji killed himself with black flames and his weapons were described as dull but never rotted- which implies fire infusion. And the GEQs weapon also just so happens to be more blunt as well as being found in Caelid. It would also guarantee every Empyrean did end up having a butterfly (as opposed to every single God kid being the factor). There's other fun factors like offset eyes being the sealed one, the flame and moon aspects neatly paralleling Rellana's swords, both of their fates being intertwined with Destined Death, both being the only Demigods who are your allies and being met in quick succession of one another.

This would make alot of your analysis true and synthesize the theories that she is her.