@Piper, I like your interpretation, but here is how I think of it:
Seven half-bloods shall answer the call.
The seven half-bloods are clearly the seven half-bloods you mentioned, so that's out of the question.
To storm or fire, the world must fall.
This part I am not exactly sure of who will cause the storm or fire, but I know that it's either rain or fire. Rain and fire are two opposing forces, so that's something to think about.
An oath to keep with a final breath,
This part means that somebody will keep an oath until they die. So it's important to remember all oaths that the characters make during the series. And no, I don't think the oath is Percy's "River of Styx" oath, since if I'm correct, he lost his power to be invincible in some book. But I don't know, because it has been a while since I last read the series, and I have not finished The Son of Neptune.
And foes bear arms to the Doors of Death.
Well, this can only mean two things:
1.) Two (or more) enemies must die.
2.) Two (or more) enemies must close the Doors of Death, which were opened in The Son of Neptune[/i (or [i]The Lost Hero idk).
The only thing we don't know is who exactly the foes are. But after seeing the cover of The Mark of Athena, maybe those two foes could end up being Percy and Jason? Just guessing lol.
But yeah, that's my theory.