First, I'm going to say that while I ship Shinji and Asuka, I don't think they had sex in episode 15 because the Japanese phrase "to hold someone tight" has the connotation of sex, much like "to sleep with someone" in English. One would not say someone else "wouldn't even sleep with me" if they had sex.

Anyway, with that in mind, the phrase "watashi no koto ga suki" is repeated in Asuka's exposure to the angel's deadlights in episode 22.

I know it means "do you like me (in a romantic sense)?" At least, the added "no koto" to the pronoun "watashi" makes it romantic rather than familial or platonic.

So regardless of whether it's the angel or Asuka herself saying it, does it reflect her romantic frustrations, with both Kaji and Shinji?

It is definitely reflective of her romantic frustrations, yeah. But almost more so than that, it is also reflective of her deep-seated insecurities and issues of self-worth, projecting her fear of being abandoned (again) that manifests as a frantic desire to have someone care about her as a person onto Kaji and Shinji as a sort of duty of theirs to give her that.
(this is not the most eloquent I've ever been, but I think/hope the idea gets across)

Also yes, the ep 15 theory is complete bunk, among other things for the reason you gave