What if the "power the Dark Lord knows not" was Harry Potter's sudden and inexplicable ability to treat the world as if it was a video game?
Orphaned Harry Potter had one more family member he could be left with: his father's squib sister, whose last name got shortened to Potts when she moved to the US.
Harry Dresden is graduated from Hogwarts, and starting his apprenticeship as a Private Auror. With the resurgent Death Eaters to fight, and a murder mystery to solve, he shouldn't also have to worry about getting dragged back into some tournament at his alma mater, right?
Luna and Harry accidentally swap lives shortly before Hogwarts. Events are inevitably altered by Luna as the Girl-Who-Lived and Harry as just a kid that gets to have his destiny unmarred by celebrity.