File it through Kraken.com, I don't think they need your MtGox password?
They do need your Gox password, they make you re-set it at the start of making your claim.
2FA is turned off (luckily for me as I lost my phone!) but passwords are still on.
Do you not have a list of possibilities that you can try? Chances are that you will need it at some point, and I can't imagine that their customer services helpdesk are still employed!