Ha, that's great! I have my own self-character as part of the wizarding community as well as others.
My character turned eleven in December, so since the school year was already half in-progress, he got the rest of the half a year to acclamate himself to the wizarding world instead. The Moonstone family was respected by both wizards of light and dark, half-blood, pure-blood and muggle-born alike. But an explosion killed his parents, so he became a ward of both Albus and Minerva for that half a year before entering his first year with the 1989 class. Though the explosion rendered him blind, he has other abilities like shadow-walking and an umbiblial cord (like a long cabled stethoscope) to read textbooks or blackboards into his ear.
As for the sorting, what I imagine is that the hat couldn't call out a house because young master Moonstone kept his mind blank. Asking for Dumbledor to quickly look over the matter, it was decided he'd be a student at Hogwarts, belonging to no house but rather to all houses as he would be the first of a fifth house along with all others who wanted such a status/his friends from whichever of the other four houses.
Yes, he did go to Olivander's to get his own personal wand, though similar to Hagred, my character had his wand embedded into his walking cane. And his patronas is a silver-plumed corporial raven.
So yeah, I've thought this through as well as you have. We're pretty much equal on the geekdom level.
*Leaves cinnamon pecan muffins for Kate.