PolyPassHash: Password storage scheme to prevent cracking passwords individually

It also presents a technique to weakly verify normal logins between bootup and when the k admins log in by essentially leaking a few bits of entropy of the user's hashed password.

This only protects against attackers accessing the password database/file from disk, not from an attack that compromises memory and the key stored there on a running server. However, in the case that the key is compromised, this is no worse than best practices used today.

Assuming the admins use strong passwords, this requires potential crackers to crack k strong admin passwords at once if they only have the file.

If you take the same passwords and protect them with PolyPassHash, every computer on the planet working together cannot crack the password in 1 hour. In fact, to search the key space, it would take every computer on the planet longer than the universe is estimated to have existed.

If it sounds too good - it probably is. Can anyone with a strong cryptography background explain if this idea has merit or if it is simply pixie dust.

Another thing PolyPassHash does not protect against is password reuse. Do not use the same password on multiple sites no matter how strong it is! We recommend using a password manager that generates a separate, strong password per site."

If they recommend using a password manager then what additional security does this scheme provide? Presumably your password manager generates strong, unique passwords.