What you could do, theoretically, is optically isolate the drive from the bridge, and have an optical splitter on the reader-to-drive direction who's signal is recorded by both parties.
They'd get a live notification of tampering, and could have independent signal blocksers that could physically block the command from actually arriving at the drive (assuming they use a few hundred meters of coiled fiber as a delay line).
The receiver on the drive side could even be a single phtotodiode, which could be made to allow easy verification with, say, an electron microscope if you're really paranoid. There are probably ways to use field-suitable technology if you only need to ensure the photodiode has the same structure as what you expect.
Cryptography won't help you with trusting hardware. Delays and intervention-ability would help, though.