I've decided to switch CDN to CloudFront from CloudFlare.
CloudFlare is free, so that's nice, but the major drawback that switching to CloudFront solves is: no expiring URLs. PrivateLog uses "private" urls to its images, but now that I've switched to CloudFront, the URL that the image tags refer to expire in about an hour. Maybe I'm just being overly paranoid, but it means that any URL that's been leaked for some reason or another won't be valid for long.