Thanks… I worked it out last night. Apparently Google Mail blocks Amazon EC2 servers from sending emails directly as there has been so much spam abuse from EC2 address ranges:
http://stackoverflow.com/questions/21087564/gmail-smtp-is-not-working-in-ec2-instance
The solution is to use a plugin that leverages Amazon’s SES service such as WP-SES. This worked for me right away.
Thanks for your response naa986! Hopefully this advice helps other users with a similar problem.