(Edit: so the match might be quick, but pre-comp of the hashes and storing them is not. how the hell would you store 1-10k hashes associated with a user anyway? :) )
You can give the user feedback on their new password choice after just one hash. The permutations would be stored from their last password set, so it would just be a simple lookup to determine whether a given new password is similar to an old one.
I'm in no way recommending this - it was just an amateur guess at a method to fulfill the requirements without exposing a massive security vulnerability.
I made the session tokens crazy long though, and have one for the user session and another for auth, and a sanity check within the auth token that will add any IP that attempts to forge the session token added to the ddos blacklist after 3 attempts. The auth token generation is slow as well - which is something that is often overlooked in webapps. I got a bit carried away in implementing all of it - but it was fun
So user feedback should be speedy enough.
Only once the password is deemed acceptable does the system need to pre-calculate the hashes for the next time the password is changed.
Of course, pre-calculating 10,000 bcrypt hashes might be too computationally expensive anyway, but the user wouldn't see a delay.
but I can't think of any other way of making 'similar to' work
Another problem is that to prevent the use of the very old passwords, you should keep the hashes of the modifications. To make the comparations fast, you have to use the same hash.
Now you have a list of #password-changes * #passwords-modifications, and if an intruder get them, it is possible to make a mini-rainbow attack.