The answer is... it depends.
But we can at least pin down the issue by name: This is a question often referred to as "substantial similarity," or "nonliteral copying."
The classic case that copyright professors make copyright students read is Nichols v. Universal Pictures. We copyright geeks call it the Abie's Irish Rose case. It was written in 1930 by Learned Hand, who in addition to having a great name, has a well deserved reputation for having written opinions that human beings often enjoy reading. (This is, sadly, a rare skill among the judiciary.) It's linked below.
I wasn't just being flip with the "it depends." Learned Hand admits as much in Nichols. That case held that the author's "copyright did not cover everything that might be drawn from her play; its content went to some extent into the public domain. We have to decide how much, and while we are as aware as any one that the line, whereever it is drawn, will seem arbitrary, that is no excuse for not drawing it; it is a question such as courts must answer in nearly all cases." (This is the kind of language we lawyers tend to like, because not only is it pleasant to read, it is susceptible to arguments on either side -- which means we get paid.)
More recently, David Nimmer (current author of the Nimmer on Copyright treatise) has proposed a methodology called abstraction, filtration and comparison for analysis of nonliteral copying. It has usually been applied to software copyright, but Nimmer himself advocates its use across the board. In a nutshell, the court is supposed to abstract the question to its component parts (which you've done to a good degree above), filter out the unprotectable ones, and then compare the protectable abstracted components to the allegedly infringing work.
The problem remains where to draw the line. The orphan who discovers that her parents were murdered by a villain and sets out to avenge their death is an unprotectable cliche. But every copyrightable work is a compendium of uncopyrightable components -- namely, words.
So looking at what you've written, those are such broad strokes that I would expect any US court to hold that it does not infringe JK Rowling's copyrights. Then again, if you were to keep to the outlines of what you describe, but were to divide and sequence the chapters precisely as JK Rowling did, I wouldn't be surprised if the court went the other way. Clearly on the other side of the line, if you were to scan and OCR a Harry Potter book and find and replace "wizard" with "solar knight" and "Voldemort" with "Galactina," you'd probably end up paying the fees of Ms. Rowling's lawyers.
As always, had this been actual legal advice rather than a mildly entertaining diversion, it would have been followed by a bill.
Copyright infringement is a difficult concept and not easily explained in a forum like Avvo. Basically, courts will look at the total look and feel of two works, and compare how "substantially similar" they are. The entire work is considered, but its unprotectable elements get disregarded. Disregarded elements include themes, ideas, facts, and obligatory to the genre or cliche scenes , called "scenes a faire," such as doomed young lovers, with a scene of angry parents forbidding the love. The original creative elements, such as tone, setting, dialogue, characters, pace, etc. etc. are compared point by point, and if enough of them align, there's infringment, especially if you can also show access to the work. Where access is obvious because, in your example, "Harry Potter" is a famous published work, then the standards for similarity are lower, and where the access is questionable, more similarity is required to find infringement.
Plot points, or "beats" in tv-speak, are among the creative elements that can be infringed, so it's not true that plots aren't part of a what's protected in a work's copyright.
Could you systematically change every aspect of a work to copy it, without actually copying any of its elements? Yes, because at that point it would be original. But if you simply mimic the plot points by making superficial changes as in your example so it's still completely recognizable as the original, you'd fool no one and get sued for infringement by the rightsholder. What you may have heard is that there are only 7 stories, such as rags-to-riches, tragic hero with fatal flaw, boy-meets-girl, loses girl, gets girl back, etc. etc., and every work is a version of one of those 7 stories. That may be true, but plot (not the basic theme or idea) is still a creative element capable of being infringed. So while "Underworld" may be a doomed love story like "West Side Story," which itself was a re-telling of "Romeo and Juliet," its use of a vampire and werewolf as the lovers, modern day setting, etc. make it different enough from "West Side Story" to not be an infringement of it, and original enough to be protectible even with "Romeo and Juliet" in the public domain.
Copyright infringement cases exist because there's disagreement about what constitutes infringement, including the protectability of some of the elements at issue, the characterization of the scenes as "scenes a faire," and the substantialness of the similarities. And this type of inquiry always depends on the specific works being compared, with the comparison always being a detailed and laborious task.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.