Thanks to @/philshapiro on Twitter I now know about https://www.pcliquidations.com and I have a new pipe dream of replacing our 10 year old computers with newer (though still not brand new) computers for less than $50 each.
I'm more likely to get funding for slowly building up a class set of Raspberry Pi computers, though, as they're already sold by vendors on our bid list. Cost is slightly higher if you include power/SD Card/HDMI to VGA adapters, but uniformity/quality has its own benefits.
Huh, so apparently the Pi Desktop CAN be installed on non-Pi hardware, so I can teach Raspberry Pi themed curriculum without having to buy a full class set of Raspberry Pi computers.
This becomes more encouraging as it lowers the startup costs significantly.