I was able to get in touch with my buddy who is very well educated with stuff like this.
He ended downloading the twitch-js-sdk file and had to make some changes himself.
He noted that the file (twitch.js) had a bug in it where they weren’t even applying the PUT method to the ajax request, so it was sending a GET request instead.
With his change applied, everything works like I want it to using the originally posted code.