You’re not alone here, Rand. While the word bisexual indicates a gender binary by its roots, that tends not to be its received meaning anymore among most LGBTQ people. Some folks choose the label pansexual for themselves if they’re attracted to more than one gender, but many more are comfortable sticking with bisexual.
As one of the members of Queer Nation working hard starting in 1990 to reclaim “queer,” I’m totally with you on the importance of both defanging the slur, and using it as a broad identity for anyone not cisgender and strictly heterosexual.
We queer people have all sorts of different interests and problems to discuss depending on particular identities, but what we all have in common is a struggle against heterosexism and heteronormativity.
That struggle binds us together powerfully, and while LGBTQ is useful to describe ourselves as a group, “queer" is a much more powerful, emotionally engaging word.
We should always keep in mind, though, that some members of gender and sexual minorities still feel traumatized by the word, and their feelings are valid and should be respected.