The problem with this method is that if one of your passwords is leaked and cracked then it wouldn't be too hard to guess how your scheme works. This gets even easier if they have 2 or more of your passwords.
It seems to me that a scheme like this would have to be much more complex, which unfortunately would just make it a pain to use.
I really wish Google, Mozilla, Microsoft, etc would step up and build a better authentication system right in to the browsers, perhaps with public key cryptography like SSH uses - then we'd have automatic logins to any site you decide to trust, and no more passwords.