@kernel, I don't think it's possible to do this kind of disk encryption after installation, and even if I'm wrong, it's probably way more difficult than simply reinstalling.
@fixit7, with FDE you can't reset the password, because you can't even drop to a root (recovery) shell. Attempting to alter the disk before the passphrase is entered will result in full data loss.
Since Clonezilla works on the OS, it only operates once the decryption passphrase has been entered so I don't see why it wouldn't work, but I haven't tested this myself.