Well, the API will help you perform infrastructure / administrative tasks such as loading new instances, monitoring their resource usage, etc. (as you already noticed). But obviously, to create your own instance of load balancing, you will need to go into any Linux flavor you choose and install load balancing / reverse proxy software such as HAProxy or Nginx.
This has been done by many, as I suspect, since most recently the Amabon ELB has become more feature-rich (e.g. SSL termination, persistence cookies).
You may find this helpful: http://blog.rightscale.com/2010/04/01/benchmarking-load-balancers-in-the-cloud/ along with the white paper mentioned in the blog post. A very common approach is to install HAProxy along with Stunnel or Pound (the last two are for completing SSL).
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