Try in mid-November, once the HS and MS enrollments have stabilized and beginner classes are set.
Barring that, buy your own. Use eBay, the classifieds, and talk to those same HS/MS directors about kids that have dropped out of their programs or graduated.
I personally own a fairly decent flute, Bb clarinet, alto sax, f horn, and an artist-level euphonium, and my primary instrument is trumpet. (And of course I have about seven of those) I've spent a grand total of $1000 for all of them combined - I paid for the euphonium. Every other one was donated by a kid who graduated, a high school friend who isn't in music anymore, or by a parent who wanted to be kind.