And now it works, because apparently the login on the Purchases tab doesn't need the full email address like on the website. It only needs the before the @ part. I had no idea.
I had no idea either. I know the login box shows in my scripts, but this part is actually managed by Rendo. I will talk to the devs and suggest adding the info to the dialog, so people don't have to guess.
Thanks for letting me know - this info may help later on if other people have the same issue.