Multiple server applications, one public IP on Amazon EC2

I have a single Windows Amazon EC2 instance and one public IP. The instance is running multiple web server EXEs which all sit on port 80. I want to have different domain names which I want to point to each server. On my old dedicated server I achieved this simply by having different public IPs, but with Amazon EC2 I want to keep to just one public IP.

I have setup several private IPs and bound each server application to those private IPs. Is it possible to leverage some of the Amazon networking products to direct the traffic to the correct private IP? e.g. I have tried setting up a private-DNS using Amazon Route53, and internally at least this seems to point to the correct servers - but not (perhaps logically) when I try to access the site externally.