I had to write an apologetics paper on Higher Criticism.
As did I, and I seriously regret not having a copy of it. There are some things absent in your post, the foremost of which is the lack of mention that the phrase "higher criticism" is a very broad term that applies to all literature in general, not just scripture.
Much of what you're referring to is, for lack of a better term, a form of hypercricism. Mainline higher criticism in regards to scripture includes applications of hermeneutics, exegetics, and related contectual criticisms. Few people, if anyone, would argue the necessity of these on their own merit. It's also important to denate the difference between higher criticism and what is often referred to as "lower criticism", which, in biblical terms, referrs to the infusion into scripture of concepts and writing to fix a prior "error" (single-translation-onlyists frequently use this to support their beliefs).
Higher criticism, when referring specifically to scripture, referrs to the application of intent of the author, the audience to whom he was writing, and the use of language of the day, including writing style, grammar, and linguistic context (note, for example, Jesus' Jesus "needles' eye" reference, or the use of circumcised vs uncircumcised to refer to jew and gentile). Proper scriptural high criticism does not downplay miracles, divine inspiration, biblical authority, or any such thing.