Appointments+ Not Syncing w/ Google Calendar

Hi, we are experiencing a problem with Appointments+ syncing to our clients Google Calendar. I have been going round and round with this problem, but never getting much for a solution.

We installed the Appointments+ plugin on and configured the settings as recommended (per the instructions online and the instructions provided by the support rep on your chat). The support rep said the issue may be with our host blocking simple phpmail function, but our host (Hostwinds) says the issue is with the plugin? I then chatted with another support rep, but he ended the chat before the issue was resolved (he recommended setting the time zone to that of the Google Calendar, which needed done, but that did not fix the problem).

This seems like it should be much simpler since we built the API to sync directly with the Google Calendar. Maybe we need to reset the API credentials and start clean?

I greatly appreciate your help.