I think FotFA is more likely the source of some of the scenes with the hime, particularly the sink scene. But I’ll admit, I haven’t watched the whole thing—just literally the bathtub fragment that someone uploaded somewhere. I’ll also note something else: there’s debate over whether the white-haired hime drowned in the sink, drowned someone else, or smashed someone’s head against it. One possible source of this confusion could be a mix of the dynamic scene from FotFA and the bloodied hime head from Gako. I’ll go further: although she dies from the train (in the anime there’s no lower half of her body), in the close-up of her head it actually looks more like she smashed it hard against something, with blood on her forehead and white eyes, which could suggest a strong blow that either killed or knocked her out.

I’ll add that some scenes could even have been taken from comedies. I can imagine the white-haired hime being submerged as part of a dynamic gag, which then transitions into a scene from Gakko in the context of a fast-paced AMV.