Have you considered using S3 bucket replication and having your application's logic fail over to the replication target in the event of a regional failure? The former is a checkbox, the latter is 30 minutes of coding (in my experience.)
With S3 replication, you still have a primary/replica setup in which only one of them can accept writes, but you can accept reads from both. So we'd gain HA between multiple regions, but we wouldn't solve our original goals: speed. The round trip to S3 was too slow for us.
Another idea might be to use Varnish for the caching layer, but I haven't compared Varnish to NginX in many years so the gap has probably been closed now?
Good work. I've stuffed this one in the back pocket for future use.
And in our case, performance between reading some bytes from disk vs memory isn't significant. A disk seek is still many many orders of magnitude faster than a round trip to Amazon.
With that said, Varnish does offer the ability to use mmaped files, but the performance is really appalling out of the box, and just not worth it. Varnish is way better if you want strictly in memory cache.
Another benefit of nginx is the cache won't be dumped if the process restarts, unlike Varnish.