You need to create another CloudFront Distribution and another S3 Bucket (www-bucket). You can use your current SSL certificate since you mentioned it's valid for both none and www
Read about redirecting from your www-bucket to the main bucket - How Do I Redirect Requests to an S3 Bucket Hosted Website to Another Host?
You can use this CloudFormation ...
private is correct, though not strictly necessary, since that's the default behavior. Specifying no ACL or specifying the "private" canned ACL is exactly the same.
private | Bucket and object | Owner gets FULL_CONTROL. No one else has access rights (default).
"No one ...
This site is a pretty good reference for using S3 and Wordpress.
Wordpress S3 Guide
It calls out some very good advantages to using S3 with Wordpress:
Reduced requests to server – because your server no longer has to deliver media files (or potentially assets), you can reduce your page load times.
More affordable storage – if you’re butting up ...
The --summarize flag prints out the summary (total objects and total size) at the end of the output. If you only want to see the summary, use tail:
aws s3 ls --summarize --recursive 's3://mybucket/myfolder/ | tail -2'