For the benefit of those hoping to find a solution to a similar issue, the fix here was to write a firewall rule on the Orion server to open port 17777 for access from Alert Central. While I had posted that the port was listening, I neglected to check the Orion server's software firewall. Once that was done, everything worked.
Alert Central is communicating with Orion using 17778 port. This means that 17778 port need to be accessible from AC.