I finally bit the bullet and tried the reset password route and it did indeed change my password for my Apple ID (the yahoo email) but also for the icloud email. Evidently they have the same password and are inextricably linked. This seems like a security problem, but at least I now have access to the icloud.com email.
To be clear, it wasn't that the email address was icloud@icloud.com, but in "Accounts" you can change the nickname of the email you're looking at and a long time ago I had set "iCloud" as the nickname for the @icloud.com email address. In the time since I did that, Apple started designating under "Accounts" a section called "iCloud" which goes to the Apple ID email (yahoo email address). So it disassociated the @icloud.com address from anything under "Accounts."
I don't know if it's possible, but I should probably delete the icloud.com address, since as I said, it seems a security problem that it has the same password as the Apple ID.