This isn't something I've tried myself yet, oddly, but if you leave your hosting server as the origin instead of setting up a storage bucket, I expect a CDN url should actually work just fine. Relative paths within the bin would just load a copy over the CDN url which would just translate back to your servers copy, and the CDN would still create a cloud of caches for serving subsequent requests exactly the same as if you'd used a bucket. XSS issues might occur if you don't set the correct origin headers up, but that shouldn't be difficult to resolve.
I'm unfamiliar with Amazon, but we do this kind of thing all the time with Rackspace CDN. I actually prefer it over storage buckets because it means you can have admin panels that upload CMS content to your web server as normal, but then the front end loads all of that content via a cloud url. No need for any middleman system to synchronise the CMS uploads with external buckets. Really, the only advantage to file storage buckets is that you don't also have to pay for a web server, but if you're building a site you'll still need a server to run that so you just might as well use it as the origin.
In fact, what I'd probably do if I were building the site, is have it just load those index.html files into iframes via a CDN url. That way the index file would load up from the cloud and all of the dependencies that it references would come in through relative paths, so also via the cloud. You wouldn't need to edit anything at all within those files, just have Corona compile a new build, upload to your server, and leave the iframe to do all of the magic.
I run a web agency and we're Rackspace partners which puts us in a pretty good position to offer complex hosting set-ups. If you're open to the idea of migrating your hosting to us, I'd be happy to take a proper look and maybe do you a quote. https://www.qweb.co.uk
. Absolutely no obligation to of course - my thinking out loud above might have been enough to get you on your feet anyway. 😏