If losing all the user table with it's "password" column is requiring you to "ask all our users to change their passwords", you're probably doing it wrong - and

If losing all the user table with it's "password" column is requiring you to "ask all our users to change their passwords", you're probably doing it wrong - and switching to some less well tested auth mechanism without the expertise to get that right either is probably just trading vulnerabilities... (If you're just requiring password changes out of an abundance of caution even though you're properly using bcrypt/scrypt/pbkdf2 - then my comment above is less relevant.)