Is it possible to have the Elastic IP (attached to the interface in the AWS console) available as the interface IP withing virtualized machine - currently eth0's IP is the private IP and the routing from EIP to the machine is done via some kind of NAT henceforth it's not possible for the running application to bind to the defined Elastic IP.
No, it is not possible. Elastic IPs are tied to your account, not to individual instances, so the instance's interface IP will always be private.
Source: this article on elastic IPs.
If this really is a deal-breaking feature, Rackspace next gen cloud servers gives you a public IP on eth0 by default.