Edit: I did not see your request even go through to the queue. Was there any errors in your browser console?
I didn't think to look. I clicked the button 3 times before posting here, and all 3 times it popped up a message indicating that the migration had completed.
I guess the message must be generated client-side, and doesn't necessarily mean what it says.
I retried after moneypot's post here and it worked that time.