Rather than using an AWS service directly (as you say they nearly all expect a much more complicated setup, deploying to EC2 etc), you might be better off using a CI provider such as Shippable, Codeship or Wercker.
These all have the ability to fire from git
updates, run build commands, install utilities into their CI images/containers and copy files to S3.
There's probably some startup which has built an exact tool for your purpose, but they haven't appeared on my radar yet :-)