My initial answer was wrong, so I did some research and I think I have a solution for you.
First of all, you're not crazy. It is really hard to add a Stack Exchange login to a preexisting account -- the option isn't currently included on the 'My Logins' page. We're looking at some better solutions, but for now, I have a kludgy work around for you:
- First, make sure you're logged in to your account. Then, go to
the account recovery
page and put
in the same email address which is tied to your current non-Stack
- Go to your inbox and open up the email you
should have just received from our system. The very last line of the
email should say
"If you'd like to use firstname.lastname@example.org to log in,
click here to set a new password."
- Click through and add a password to associate with your email address.
- Head back to your account, go to 'Edit Profile & Settings' --> 'My logins' and check to see if an SE OpenID is now one of the options.
- Success! (hopefully...)
Let me know if that works.