most of my identity isn't covered by "LGBT", but I still find myself legitimately irritated by the ever-expanding initialism, even when one of the added letters describes me. It's missing the point that you describe, and it's also wildly impractical.
I'd very much lean towards a phrase like "queer community" if not for the fact that I occasionally find people vehemently opposed to being called queer. I don't know much about when the word was used as a slur -- that seems to have been before I really started interacting with other LGBT+ people, and I somehow missed most of the *-phobic spaces growing up. But it definitely feels like the only existing word that fits.
I've always felt that the popular "LGBTQ+" was good enough. It covers everyone, most of them at least twice. I lean towards LGBT+ because the + fills the role of the Q, I don't have to worry about the aversion some have to "queer", it still has the recognizable "LGBT", and it's a little less typing.