Just subscribing to this thread and saying I’m having the same issue with our shop; when updated the plugin takes our entire site and admin panel offline (HTTP ERROR 500).
So I’ve misunderstood the guys here at some point, we’re just using ELB with Amazon and not Cloudfront. However, we switched it back to Automatic Download mode, and with the updated “External IP of this server:” tool now detecting Amazon’s IPs and the body class name is now correct!
Thanks Benjamin! I’ll reply asap; our WP has a filesize limit so I’m having to send the plugin to someone who can upload it directly to our WP folders.