It looks like I've fixed the problem.

I renamed the folder on the server to the 2nd name I chose for the task. (I already tried deleting the task and creating a new one with the same original name.) Then I created the task again and called it the 2nd name I chose as well. After refreshing the task list, it finally said that it was partly backed up. So I started the task again, and now it's incrementally backing up, which is great.

It seems that whatever data is stored linking the task to the online folder remembered the 2nd name, not the original name. When I ran tests on a very small backup, this wasn't the case. I had to create a new task with the original name.

Anyway, it's fixed now. Thanks very much for the advice!