Can't reset password for email credentials when logged in via OpenID

I log into SE with a Yahoo OpenID, which I have to stop doing by July.

I apparently also have an email/password login. I don't remember ever creating one (although maybe that's what I used before SO had OpenID support?), and I certainly don't remember the password. And there doesn't seem to be any way to reset my password when logged in via OpenID. And the way to reset my password (account-recovery; thanks to Adam Lear) was not discoverable from anywhere I could find. Once you're logged in (via OpenID), there's no links to account recovery anywhere, even on the pages asking me to enter my email and password.

If I go to My Logins, I see two entries: Stack Exchange and Yahoo. The first one has a change password link.

So I click change password, and I'm taken to a page called password-reset, which looks like this:

It requires me to type in my current password. Which I don't know. There's no link anywhere to send a password-reset email, answer a challenge, or do any of the other usual alternatives.

This page could just have a link to account-recovery.

If I go back to My Logins and instead click add more logins…, I'm taken to a page called login-add. This page tells me "You are currently logged in as abarnert. Add another way to log in using any of the following services." And then it has this form:

This is an odd form for adding a login—i.e., registering an email and password—given that there's no confirm-password field.

I'm pretty sure this is a bug. But maybe I'm supposed to enter my email and desired password, and I'll be asked to confirm it later? Nope, I try that and click the Add Login button, and I get the error The email or password is incorrect.

I've tried searching around for other ways to reset my password, but everything I can find (links on the above-linked question, instructions on this question, etc.)) ultimately takes me to one of the same two pages, where I can't add an email because I already have one, or can't reset my password because I don't know it.

I also get the same behavior if I try it on a different network site instead of SO. (Unless I try it on one I've never visited before, but then it first requires me to login to connect to that site, which I can only do via my Yahoo OpenID because I don't know the password for my other login, which leaves me in the same state.)