Figured it out - I was able to get SES to work directly through ZenCart via the ZenCart smtpauth setting (no need for exim or sendmail).

Overall AWS EC2 works very nice for a ZenCart site and the pages load very fast. I'm also using a Global Accelerator and Application Load Balancer. The Global Accelerator provides two static IP addresses. My purpose for the LB is to make it easy to get and automatically renew an SSL cert. Using GA, I was able to register one of the IPs with the domain A record.

It just takes time to navigate through all the AWS menus and learn how to configure everything. I like EC2 better than LightSail because LightSail is glitchy.