Options 1 and 2 as insecure as each other.
There. I said it. If the user's email account has been breached, there's no reasonable secure way to do things unless you collect more private data like their address, mother's maiden name - all of which can be guessed.
The best (albeit most annoying) version I have seen is where you need to remember a secret question and a secret answer. It means the user has to remember which question they asked, which, of course, can always be forgotten too!
If they forget the question and you're a "real" company, there's always the option of sending the user a token through the post, with instructions on how to reset all their security... It's very unlikely that a hacker will have access to their real life mail.
A skew on that would be to collect a telephone number when the user created the account. If that existed and they couldn't remember any of their details, you could set up some sort of automated calling system that told them how to reset their details.
And one thing to mention about #2: Don't let the process overwrite the current account password. If that happened anybody could say they forgot any account's password, triggering lots of unwanted password changes.