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Could you hash using both, your preferred algorithm first then theirs? That would make everyone happy.

bcrypt(sha256(pw)) works I believe, but it might not be enough to satisfy the policy.

It's actually better than plain bcrypt because you can allow long passphrases.

Is it better? The suggestion is vulnerable to a sha256 collision attack.

Except that for a collision attack to be a thing, you need to know the value you're trying to collide with - and that requires reversing bcrypt.