Thank you for the link and for the suggestions. It will take some time to review everything to figure out what/where/why things are not working as desired.
Plan now is to have someone with more experience than I in Exchange 2013/Online review the setup and get things working.

It's hard to tell if you read my post, since some of my questions cover things I already said in my first post.

YES it is a hybrid configuration and YES this mail server can receive email from OTHER O365 sites, just not our own O365 mailboxes.

All default and O365 connectors are already configured.

Wrt disabling Barracuda email security -- how do you propose that I do this?? Furthermore, no one would receive ANY email if I did this. :)

Regarding the message tracking, the above-posted log entry DOES come from the receive transport log within the Exchange server itself.

Finally, it's not exactly a 'blocked' issue. It's a NOT AVAILABLE issue. The Wireshark packet and the log clearly say "Service not available" referencing the SMTP service.

WHAT is making the SMTP service not available?? WHY is this message occurring??

Thank you, TOm