The most bitter thing is: your story is nearer to reality than the tribe JKR sprouts about.
What I'd like to see is a Harry that left the country to an other former commonwealth one, and on entry is detected as magical, brought to the 'muggleborn'-immigrant attendant and carefully asked the needed questions for a direct immigration. Taken great length to bury the paperwork as deep as possible, Harry (given a new Name) is placed at a combined school (magic/normal). Cue to a frantic search for "Harry Potter" who, -- as far as magic is concerned, -- no longer exists.