Meg, it seems you've put a great deal of thought into this. And despite being slightly sad to abolish the house system, and therefore take away the amazing magic of it, it makes a lot of sense to take it away.
I think it would be nice to be sorted privately at the end of seventh year, as Sydney said.
I think that students should still be sorted, for Quidditch and House Cup purposes. But if they are the only things affected by the houses (new ones, too, that are randomly sorted), maybe there would be a tonne less prejudice. If less focus is placed on the cup, then students won't be that worried about what house they're in and who wins. Of course they'll care, but it will be vaguely forgotten about after a few weeks - like Muggle schools. But it still makes me sad to take away some of the magic of Hogwarts *sigh*
~ Annalise x