(It's not actually 'Fuck You,' but something similar and I do sometimes change it up with a few different simple phrase answers. I did own an 88 Cutlass Supreme [worst car I ever owned], but it wasn't my first car.)
Maybe that should be a security question, "what the worst car you've ever owned?," now THAT'S easy to remember all the times you're stranded on the side of the road, stalling in the middle of heavy traffic, and all the repair bills.
Problem with "other password approach" is "I just put a bunch of random characters in there" becomes a valid response to an overseas customer service rep if you're talking on the phone.
EDIT: Ok, any English word or phrase would work for "other password" just fine. I guess after idk how many years of trying to use the "secret questions" as intended I just get angry every time I see them.
Just kidding... your approach is a good start, but use a unique password for each one instead of "fuck you".