You could try and start sync gateway with the ports bound to all interfaces:
sync_gateway -url http://localhost:8091 -adminInterface 0.0.0.0:4985 -interface 0.0.0.0:4984
If that solves your issue, you can then change the public REST interface IP address to bind to the specific public interface of your AWS instances. You would want to limit access to the admin interface, so you could either bind that to localhost (127.0.0.1) or to the private IP address of your AWS instance.
Andy