I don't want to use a peer-to-peer network to hide information.  This parallel blockchain would openly store the 2nd encrypted private keys.  Anyone could look at them, no one would have a clue what the actual private key is due to the encryption.  Importantly, this network enforces your rules as to when this 2nd extra key can be decrypted.  It reaches consensus among a majority of users so someone with a rogue client can't artificially set conditions to reveal the true private key ahead of time.  By the time it finally does decrypt your 2nd private key, it has already forwarded the transaction to the bitcoin blockchain.

The ultimate point is that it allows you to enforce a spend delay on the coins before they even go out of your wallet.  Whenever someone tries to move them you know about it + can do something about it before they're gone for good.