Harry Potter and Hogwarts U

What if Hogwarts had to wait to start till student's were 18 when their magical cores matured? With magicals going to the Saint Schools for primary/secondary, they have a big lead on the Muggleborn in everything but magic. Follow Harry as he leaves Stonewall behind to enter into Magic where the rules seems stacked against the Muggleborn/raised. AU with alternative sortings. Harry/?