There is no "third way". End-to-end encryption means no one other than the sender and the intended receiver(s) can access the decrypted messages; full stop. That includes the social media companies and the government. This obviously also precludes hacks like subverting the client software on either side to report back on the content of the messages (i.e. Apple's implementation)—if the user can't trust their client not to deliberately leak details about the message then they don't have E2EE, since someone else's agent has been placed in the communication path.