awsarch went SSL.
Amazon offers free SSL certificates if your domain is hosted on an ELB, CloudFront, Elastic Beanstalk, API Gateway or AWS CloudFormation.
For more information on the Amazon ACM service.
So basically it required setting up an Application Load Balancer, updating DNS, making updates to .htaccess and a fix to the wp-config file.
Now the site is HTTPS and the weird non-HTTPs browser messages went away. Come July Chrome will start carrying a warning sign per this Verge Article.
Free SSL certificates can also be acquired here https://letsencrypt.org/