In Ham radio, you can't use any sort of secret message like that. Everything needs to be plaintext.

I don't think that's correct. Cryptographic authentication of messages should be allowed (ARRL agrees with me[0]), the language specifies you cannot "obscure the meaning" of the communication.

0. https://ecfsapi.fcc.gov/file/7520928844.pdf

That's correct. There's one exception to the encryption rule, which is when sending commands to a space station. (That does not allow you to encrypt the responses, though.) See 47 CFR 97.211, https://www.law.cornell.edu/cfr/text/47/97.211

Well, I think then you'd be breaking protocol, because afaik, in ham code you must obey procedure, and QRT tells you to stop transmitting.