Proof that a encrypted file has the same content as an (existing) original
Retaining the 3DES encryption key would probably do it. Now simply use the same IV as before and encrypt the file; the IV is only random when it is initially chosen. Alice could also encrypt the key and store it together with the message.

You'd have to prove that you used the same key. That's no problem for larger messages in CBC mode where the possible plaintext is known, but for good measure, I'd include a MAC over the IV and ciphertext in the mail header.



Alternatively, and possibly better than using a MAC, is to transmit the random padding with the message and store the secret key. That way you can regenerate the wrapped key by pairing the padded key with a raw RSA operation, proving that it was that specific key you used.

It might be better in the sense that creating a covert channel is harder if all the information is shown to Mike. It has the drawback that it requires access to raw RSA operation, which may not be directly available to you.