[cnvogel]

Yes, that's certainly a solution.

Or using a certification authority for users (TrustedUserCAKeys in sshd_config), so that any user that has a signed certificate, and owns the corresponding private key, would be allowed to login. No further updates of authroized_keys files needed.

And, to further automate the ssh login, maybe your LUKS container could have a second (Nth) key-slot being a random key RSA-encrypted with the other machine's identity private key? (https://bjornjohansen.no/encrypt-file-using-ssh-key for examples)

But generally, I really dislike the use of LUKS in this case, as I think a filesystem based encryption (not encrypting whole block devices) would make more sense. I understand that this isn't as mature as LUKS, though.