Why don't you use standard Key derivation function PBKDF2?
PBKDF2 (Password-Based Key Derivation Function 2) is designed for password inputs. We don't input password, but a long, random number. Even more importantly, it does not offer derivation of public/private keypairs. Bip32 does.
Bip32 is used in deterministic (bitcoin) wallets. How does your scheme relate to that?
Key derivation process is the same, usage of key-pair is different;
bitcoin deterministic wallet
ZeroPass Backup tier
Master Private Key
Used to transfer/reconstruct whole wallet within different services.
Gets split/distributed and then erased. It can be put together if you lock yourself out (recovery procedure).
Master Public Key
Used to generate (child) public bitcoin addresses without exposing private keys.
Used to encrypt all your passwords (with his child keys) that can be decrypted only with (at this point already erased) MasterPrivateKey.
We can then safely sync MasterPublicKey between devices. Even if it gets leaked... it's Public key, it can not expose anything.