Newly healed scar, new name, new country. Harry, 17 years old and a newly-minted war hero, fled Britain. He couldn't take being reminded of everything every day, and without a complete education, he had basically no prospects. So, with the help of some discreet and sympathetic people, Harry starts over in America. As John Sheppard.
Flying is and always will be his truest love, so he got a degree in applied mathematics and then he joined the air force. Then he went to war. Then he didn't follow orders and got banished to transporting people back and forth across Antarctica.
Then John sat in a chair. He was more than a little alarmed when it did things no one else seemed to be able to make it do, very visibly and in front of a lot of very important scientists responding to his magic. But they didn't assume magic and they said they needed him and without enough time to really even consider saying 'no', he was dragged along on an intergalactic journey to the city of Atlantis.
And then, he somehow started another war.
(this verse pushes back the hp timeline by a decade)
(Harry was adopted by Natasha during his fourth year (he didn't notice) so Umbrige didn't last long, Remus was Defense professor again for most of that year, Sirius was killed in a separate scuffle with Voldemort's crew, and Harry killed Voldemort with a gun.)