It seems improbable that the booming school equipment business of Diagon Alley survives on one school's worth of customers, especially if most of them only shop once a year.

It didn't seem to me there were so much school equipment business. If you look at the shops Harry went to the first year, it's a dress shop, a book shop, a wand shop, a potion ingredient shop, a broomstick shop, a pet shop, ... none of them sound dedicated to school equipment. They probably have a lot of school equipment in stock/display during august, like supermarkets do here too, but continue selling their goods to adult wizards the rest of the time.

The rest of your objections do hold, but I just fold it into "canon HP isn't very consistent" suspension of disbelief... of course, it makes things tougher for EY when he's making a consistent version of it. But that's part of what makes HPMOR funny/interesting.