Which worse? Your SIM as an alternate password, or public information about you being your alternate password? ("Security" questions and "identity verification")

You don't have to give true answers to security questions, FWIW.

Yep. All of my answers are GUIDs that I keep track of in 1Password.

I have read a suggestion that one should pick real (but randomly generated) words because, where it is possible to call the company that maintains your account, an attacker might claim that the recovery answer is a series of random characters, and there is a chance that the employee will accept this and allow the attacker access to the account.

I thought this was a good strategy too until some one said that a customer service rep once asked him one of the questions over the phone and, lacking his backed up security questions at hand, he just said "it is a bunch of random characters" and was let through...

Probably the best bet is using a passphrase here but it might not be fool proof.

I've started to make up answers that could be accurate, but aren't obvious / the first thing someone would guess. For example, if the question is "where were you born?", I pick a random city.

How about no alternatives? The password being the only authentication mechanism.