Well, maybe next time.
In a vacuum, if such a viewing would be possible at all, it would be an all right samurai fantasy action film with an appropriate amount of thematic exploration regarding isolation and loneliness when it comes to Hitomi's depression and Van feeling like he has to shoulder the weight of the world on his own, doing it in the only way he can: By fighting for what is by all accounts a lost cause. Not particularily something I would turn on because I want to see it, because there are other films to choose from that would be better watches overall (not necessarily more enjoyable, but this is an area where watching Japanese live action films clearly yields better results), but equally nothing I'd turn off immediately either.
As Escaflowne, indeed, this is just terrible. It's character assassination of the worst sort, removes everything that made the original lovable and arguable unique and replaces it with an equal amount of serious, gritty and bleak.
外伝 (side story, sometimes used to mean spin-off, but literally more like outside legend, 外 is the same kanji used to spell the somewhat pejorative word for outsider/foreigner gaijin - 外人) stuff is pretty popular for a whole lot of things. I'm not sure, but the ones I encountered at least all had the sense to not be retellings set in the same universe using the same characters, but rather perhaps using the same characters in different settings or making actual side story in a similar or the same universe. One of my most favorite Gameboy games is one of those, Final Fantasy Adventure. It became the basis of the Secret of Mana series.
Anyway, The End of Evangelion is more like an actual narrative ending to the series. It works as a replacement for the last two episode, it arguably works in tandem and/or parallel with the last two episodes of the show, I'm not sure I'd call it a traditional side story, and I also really don't think Escaflowne counts either, but hey, if people want to label it like that that's fine with me. It's still a bad Escaflowne film and would improve immensely by letting the characters - and the film - stand on its own.
It might be that Perfect Blue looks like something else or was inspired by some other film, for that I don't know enough about anime films in general, it's mostly Hitomi's character design and animation, that did remind me of Mima a bit. It's not entirely fitting because the eyes are drawn rather differently, but everything else fits. As for many of the scenes and influences, if you want take a look at the scenes from The Seven Samurai. While that's live action, does that remind you of something?
edit: I mean some of the action setpieces and general looks, not necessarily the plot or anything else. Escaflowne is still a fantasy piece with a bit of a sci-fi bend, all in all.
Pretty much.