Block cipher birthday bound and a KDF workaround Can the birthday bound arising from a block cipher’s block size be worked around by deriving different keys from the master key with a KBKDF using a tweak?

For example consider the following scheme, which assumes


K is a 256-bit key
tweak is an integer we can increment before 2^64 blocks have been encrypted with the current generation


and then encrypts as follows:


IV = random 256 bits
EffectiveKey = KDF(K, context=tweak)
ciphertext = KeyGeneration || IV || AES-CBC(IV, EffectiveKey, plain)


Would this scheme be secure for encrypting more than 2^64 blocks?

Asked in order to learn more about the birthday bound.

EDIT - this has similarities to the construction used in the Better Bounds for Block Cipher Modes of Operation via
Nonce-Based Key Derivation paper (great talk too by Yehuda Lindell), which also introduces AES-GCM-SIV.
Obviously you assume blocklength is $128$ bits. I believe the following is correct.

One might try rainbow table TMTO attacks, assuming known plaintext, and succeed with time and memory complexity somewhat better than
$$
O(2^{(2/3)k})
$$
where $k$ is the effective keylenth,
against such a scheme but it would be secure beyond the birthday bound.