I'm experiencing the exact issue described here. I have a Google account whose primary email address I have successfully changed. The account also has an activated backup email address. When visiting Google Alerts, I can't edit the Deliver to address. The option is greyed out and the value is an old email address that is no longer associated with my Google account.
I have added additional email addresses, looked for any mention of the old email address but I haven't found any and tried to contact Google. Google doesn't seem to have a contact form, beyond the forum post on their community forum that is linked above. Any help with changing the email address would be greatly appreciated.