Also, I don't know if this is helpful but I am also unable to migrate that one user's mailbox back to on premise. It fails with the error TransientFailureTarget and gives similar network socket errors that the Connectivity Analyzer returns when I look at the XML report file. It's like my on premise Exchange 2016 refuses to talk to the exchange server that this one user is located on. Yet there is nothing in my firewall that would prevent that. It's also not a TLS 1.2 issue as I made sure that was setup a long time ago.
I created a test user in 365 and was able to successfully access on premise free/busy just fine. I was also able to move that mailbox to on premise just fine. It is something with this one user I just can't figure out. Again, I have support involved. If they figure out the solution I will definitely post it here.