What happens if I overwrite the start of a LUKS partition or damage the LUKS header or key-slots?
There are two critical components for decryption: The salt values in the header itself and the key-slots. If the salt values are overwritten or changed, nothing (in the cryptographically strong sense) can be done to access the data, unless there is a backup of the LUKS header. If a key-slot is damaged, the data can still be read with a different key-slot, if there is a remaining undamaged and used key-slot. Note that in order to make a key-slot unrecoverable in a cryptographically strong sense, changing about 4-6 bits in random locations of its 128kiB size is quite enough.