Also, I can't tell you how much I hate that "cloudflare" sounds so much like "cloudfront". I've been in at least 6 convos where people were mixing one for the other. Esp, since they solve some of the same problems.
Then I realized, oh they said cloudfront. So you could still technically keep your stuff in your S3 bucket, though you'd end up paying more for S3 originating transfer as well. In this case, cloudFRONT (the non amazon one!!) may be the better choice.
Hate that they sound the same. I even get my OWN THOUGHTS mixed up sometimes :(