I was also concerned about this issue, and have instead taken a nice medium path: After changing a password, I would try to log into the service at approximately the same intervals the Anki algorithm dictates until I feel the interval is long enough (i.e. I can reproduce it after two weeks with no reminder, which corresponds to a forgetting curve of about a month later). Just because I won't use the program doesn't mean I won't use the idea!
Ideally I would have a reminder in my Anki deck to log into some service, but I spend most of the time on Anki via phone and it'd be a PITA to stop my current session and laboriously type out long passphrases on the tiny iphone screen.
I'd be interested if anyone else has found a better solution than this.
I use Flashcards Deluxe, whose data is only on my phone. After memorizing the password, you can remove the cards. If one is really concerned about security, you can just install a safe password manager and only leave the prompt on the flashcard. For example:
This could be a huge problem if your phone/laptop/whatever is stolen.