I'm using Ember FastBoot to render the site on the server, so it's not quite static. For some reason it's throwing lots of errors and dropping requests right now, even though it didn't when I launched Indie Hackers on HN last month and had about 3x as many requests/second. Frustrating.
Anyway, I'm in the process of just moving it from Elastic Beanstalk to serve it from S3 via CloudFront directly. Waiting for the CloudFront distribution to spin up...
If you use a service like netlify, you can host a static site for free on a CDN. It's actually really convenient because it can build the site automatically whenever you push to a Github repo, and it can automatically setup HTTPS for you with a Let's Encrypt cert. It's a lot easier (and cheaper [free]) than setting up S3 and CloudFront yourself.
Github pages can do the same thing - it just has fewer features.
Good luck, though it looks like you're making good progress already. Last time I had to wait for CloudFront I sat there thinking "this would be a real pain if I actually needed it now..."
Anyway, I'm in the process of just moving it from Elastic Beanstalk to serve it from S3 via CloudFront directly. Waiting for the CloudFront distribution to spin up...