(By "principles" here, I mean correct ones.)
That there is really no nuance or context in her novels (or other work) follows fairly directly: these are idealized, metaphysical types, and an empirical or inductive methodology is nowhere in sight. She occasionally claims something about induction, but does not actually follow any such methodology, certainly not in any rigorous fashion.
Can you point to one actual claim made by AR that is in common with Nietzche? I seriously doubt there is one.
Going away from actual claims to mere generalities, yes, AR and Nietzche were both "individualists" in a sense - but in a totally different one. Nietzche in a predatory way, AR in a "mutual trade for mutual benefit" way.
she does not deduce principles from reality, but from metaphysical first principles
She doesn't decduce, she induces, and she does not do it from metaphysical first principles at all. Her core metaphysics is axiomatic, but the rest of her philosophy is inducted from reality. Most of her philosophical essays are just summaries of the results of this process. There is no work that "competely induces" Objectivism. There are a couple of works by Leonard Peikoff that talk about the Objective process of doing this. Until recently, they were only recorded lectures, but "Understanding Objectivism" was just released as a book.
That there is really no nuance or context in her novels
A lot of people don't "get" the novels. Just a few days ago an Objectivist was telling me how mind-blowing Atlas Shrugged is, because there are about "12 layers" (quoting him) of meaning in any given chapter. You would be surprised. It does not appear to be this way on the surface.
The problem with using her novels as an argument for the position is that they only really work in an affective, sense, imo, as implying consequentialist arguments, sort of along the lines of a morality tale or fable: look what could happen if things are done this way, or alternately, if they were done that way. And I think a lot of people do read them that way; the famous "going Galt" plot, for example, is commonly taken as a parable for why bad things will happen if you institute too much regulation and burdening of productive individuals. But she explicitly disclaims "things will turn out better/worse" as a reason to accept or not accept her philosophical/political views, so her novels aren't supposed to be read that way. But they're actually more effective that way! Which is why I think it's so common for fans of Rand to ignore Objectivism and instead read her as more of a general pro-free-market, libertarian author.