These guys are $200 a pop.
That's the problem. The OP is looking for something substantially more affordable. It's easy for those with some reasonable income to not realize just how tight things are for the poorest members of society.
That said, I think there's a real limitation as to what can be achieved at such low pricepoints. At about the $170 range you can have a decent screen, processor, storage, and RAM. As you go below that price point things have to be sacrificed. Unfortunately I don't see much in the way of screen-less options that save money. HP make a Stream desktop that runs windows, but it's still around the same pricepoint. Intel make a compute stick, which is better with a $135 price tag on Amazon, but that's probably still too expensive.
Maybe you're stuck with something Raspberry PI like, with a small but fast SSD and a cheap case, keyboard, and mouse. That sounds like it could work, but once you have the computer, case, HDMI cable, SD card and some sort of removable storage so the kids can submit work, you're still going to have a price tag that is well above $50/head.