When explaining the concept of signing a message, often it is presented as "encrypting with your private key", so that somebody who has the public key can "decrypt" the signature and verify it. However, PGP signatures (especially detached signatures) allow you to read the plaintext of the message regardless of whether the signature is valid. This might not be desirable in some cases -- for example if there is a chance that the receiver might not want to verify the signature properly, but the message is important enough to warrant requiring such verification.
Is there an option for "real" encryption using the private key in PGP -- a way of signing a message such that if the result is tampered with, the plaintext of the message cannot be recovered?