Solved it. With a little help from the internet. Well, maybe a lot of help.
Open and verify an account (free) on last.fm, then open Preferences and set up a photo for your new account. Save it.
Return to the profile set up page on the iPad. Sign in to your new last.fm account. Hit save, and the photo you uploaded to last.fm fills the profile picture space.
Only took me about four hours (four hours!) to get it done.