thanks for your investigation!
The options above are just general guesses how to it could be achieved. I have no idea if this could work the Edison/Galileo or how it could be achieved.
Many years ago I did a undervolt treatment with my Pentium M in Linux. When I remember it right, there was a kernel patch to achieve this. However, I don't know if this would work for the Edison/Galileo Platform.
Are there any resources/general advices on how to reduce the power consumption on these Platforms?
During the prototyping stages for e.g. it would be nice to control the Atom/Quark from the Arduino IDE. For e.g. to put them to a deep-sleep state from the Arduino IDE and wake them by timer or or with a interrupt coming from the GPIOs.
It this is not possible within the Arduino IDE it is maybe when working with Python, node.js or MRAA + bash scripts?
About Galileo, take a look at this document (Section 8) you will find helpful information about Power Management. Unfortunately there aren't tests of doing this but I think you could try a couple of things with the S states and others.
About Edison, we are working on more documents and information about Power Management, there are no ETA but you could try your suggestions above also in the WiFi Guide (Section 7.1) you would see how to disable the power management