Yes, it turns out the grader will only grade the “official” name of the notebook. Even if you do happen to get a “Submit Assignment” button in a different named notebook, clicking that will grade the one opened by the “Work in Browser” link.
So you will need to choose which notebook you want to grade and then rename it back to the normal name. If after the rename you still don’t see the button, then do “Kernel → Restart and Clear Output” and that should bring it back.
Thanks. good to know. Will give it a try.