I'm surprised that
A) Harry mentions avoiding being detected doing underage magic. If he has to worry about that, why not go home and start casting spells with the wand. Then he can be expelled from Hogwarts AND get the auors to remove the compulsions on the muggle headmaster.
B) WHy would he spend his money on school supplies? He should just show up in the clothes he'd wear to Xaiver, and when somebody objects, say that as he didn't sign up for Hogwarts but was forced by Dumbledore using charms on his other school's headmaster, Dumbledore should assume all the costs associated with Hogwarts, since he's taken the choice away. I don't blame Harry for buying the other stuff, but not the school supplies.