The API quota for my project was successfully increased to 4M through the application process. This is confirmed in the details for the quota via the Google Developer console quota page for the enabled API.
Videos are, however, being rejected with this message after just the standard 50 uploads with this message:
Task 310: Upload failed. Exception: HttpError 400 "The user has exceeded the number of videos they may upload."
Here is an example of a successfully published video.
Thousands of videos are waiting in the queue from an event that finished days ago. Several people from Google have been trying to help but this morning I was asked to post on Stack Overflow.