Hi JeremyTBradshaw , yes, that is correct, the Basic FB test will return error. But the Modern Authentication FB test can reveal some issues with DNS, certificates and autodicover. At start it will indicate where source and destination mailboxes are hosted. Some firewall issues can be seen there.
I dont expect you to have firewall issues, as you do have Free Busy working for Exchange 2016.
On the autodiscover part it should show the Front End server that replied even if the xml is not provided. To follow logs to find errors that's where i start.
One thing came to my mind. Is the current Auth Certificate distributed to all servers?
You are using IOC. Have you tried with Federation and Organization Relationship? Lookup method is a bit different and may work without much changes to your configuration. Exchange Online is nativelly Federated and Federating an on Premises Organization is quite simple.