EC2 is inherently scriptable. There's nothing stopping you from using the command-line tools to fire up an instance, and let it run, and store its results to S3, and then decommission the instance.
You are correct that what you propose is easy and well documented. However, that is not what the OP needs.
The OP needs lower-priced spot instances, which are intermittently available and designed exactly for this workflow. When the entire AWS datacenter has some spare capacity, these spot instances turn on for those who requested them to run (usually to crunch data that is not time-sensitive). The use and configuration of these instances is not so well documented, probably because you cannot run a webserver on them and that seems to be the focus of much AWS documentation. However, it is exactly these 'spot instances' which are in my opinion the genius of the cloud: they let the heavy, non-time-critical work (i.e. scientific computing) be done when the webservers and mailservers aren't so busy, thus flattening out the daily CPU demand curve.
The OP should start here:
http://aws.amazon.com/ec2/spot-tutorials/
And end here:
http://docs.aws.amazon.com/AWSEC2/latest/UserGuide/tutorial-spot-adv-java.html