Sorry for the confusion here... we're still missing some overview documentation that may have made this clearer.
For "content-style" endpoints like upload and download, the JSON is passed in the "Dropbox-Api-Arg" header, not in the body of the request. Take a look at the example curl requests in the documentation to get the hang of this.
So you'll want something like this (completely untested):
As another tip, I'd say you should always read the body of the HTTP response when you get an error. The body of the 400 from the API will generally tell you exactly what's wrong with the request.
We love to learn from the educators who use Dropbox. Whether you teach kids, teens, adults or a combination of all three, we want to know what apps and integrations you use with Dropbox to help with teaching. Which of the ones below is your favorite, or most used tool?