For example, you manage to 1CC the game on pointdevice mode... but because you have tainted yourself with the ultramarine orb medicine that Eirin gave you to achieve your 1CC, the stage 6 boss could say something like "you are unworthy to face me in my truest form, impure one" when you beat her and you get a normal happy ending.
You suggestion would only make sense if it isn't a 1 Credit Continue. Getting hit even once is considered a flaw. That is the whole reason why you have the Point Device mode, so you can beat the game without getting hit once.
Now, if you were to 1CC the game in Legacy mode in normal difficulty or above, you can prove to the one that is behind the moon invasion that you are a pure being just like they are that douse not need special medicine to stand up against the lunar defenses. Once you beat the regular stage 6 boss, the boss character will recognize your skill and/or "purity" and decide to unleash her "purest" form.
In order to do what you suggest, the player would have to beat the game without getting hit once. Such a mode for an extra ending seems pretty hardcore.
To be honest, I doubt it's either of those pairs, if it's gonna be a pair to begin with. They seem too obvious and deity-like. You didn't fight the Buddha in UFO, either, even if people could've guessed that based on the TH12 demo.
But you fought a god of the highest tier (Eirin), whose students were Yorihime and Toyohime. So, there is already precedence.
Yorihime/Toyohime aren't going to be characters that we fight against in this game, main game or extra.
As Clarste has mentioned, extra is unrelated to the plot, so it wouldn't matter.
That said, they could also be a candidate for stage 4.
Ultimately, it is unlikely for these two to be fighting the protagonists, but I wouldn't rule out the possibility.
To be honest, since this is a major incident and your life is at danger, it doesn't feel right for them to solve it individually.
They are using the Point Device, so that argument is invalid. It is still possible that they are solving it together.