Key recovery after AES-ECB encryption of two blocks with some known plaintext/ciphertext
With the encryption of the Temporary Data with 64 bits of plaintext known, does this allow an attacker to brute force the password and know when they got a plausible password because the decryption of the Temporary Data with AES and the derived key they are currently trying will result in 64 bits in the middle being zero which is statistically unlikely?


Yes. The attacker tries plausible passwords starting from most likely (1234, test), runs each thru the password KDF to get the corresponding Password Derived Key, use that to decipher the temporary data, and check that the appropriate 64 bits are zero. If that's the case, the right password has likely been found. This is selective enough that for a fair quality password (says 48-bit, more than XKCD propose), probability of false positive are low ($\approx2^{48-64}&lt;1/65000$). Because there is no salt, the cost of the password KDF (if sizable entropy stretching is used) is incurred only once per password, regardless of the number of users (each user targeted add obly one AES decryption and test).


  Does this mean they could use that recovered Password Derived Key to decrypt the Master Key?


Yes, and from that the "data on the service".



With what we know, I see no other attack, and it is unclear what's the baseline for "more easily" and "less effort" in the question. Forget about brute-forcing AES-128. If there was known plaintext or redundancy in "data on the service", that could help (e.g. to confirm the password), but won't change the overall attack cost, which depends mostly on the password KDF and its parametrization; and the user choosing a hard-to-guess password.