Ok, I’m still not clear on exactly what you’re trying to achieve as I can’t quite see the connection between somehow preventing certain files being duplicated when cloning the disk and preventing yourself from reinstalling the system.
Bear in mind that reinstalling the system would replace all of the OS, so there’s no way to leave counter-measures there, and the disk itself can’t do anything to your data, even if it could detect a clone operation.
If what you’re trying to protect against is someone who knows everything you do accessing your data, you could look to use TPM to store the encryption key for your FDE. That way you don’t know the password, it’s stored encrypted with a secret key that is, in turn, stored and protected by your CPU. That way a disk clone couldn’t be used on any hardware except your specific machine.