Well, this is what I came up with...
Get yourself a temporary email address, I used http://www.guerrillamail.com . Click your existing email address on the top right (may not be click-able from this page, but it is from the products homepage - gotta love the consistency here). Put rubbish into the fields as appropriate as you'll be abandoning this account.
Then go to "email address" and change the account email address to the shiny new temporary account you created. There'll be the usual confirmation email with code things, truly un-inspiring. Enter the code and complete the email address change.
Your real email address is now available again to create a new account with so you can add your new details. Your previous account is not, in reality closed, but as that function doesn't exist Sling can't complain that it doesn't happen.
Details "update" complete. Whoo!