Thanks for your interest in the project!
Alright: here's what I have in mind.
I have a 4 aa battery holder, and I'm going to step it up to 5v, 3a amps with the following thing I found on ebay:
Dual USB Solar Boost DC DC 3V Step Up to 5V 3A Module | eBay
The battery holder is able to be charged all at once by a solar panel. Then, the holder outputs to the voltage regulator which output to a stripped down usb cord that connects to the power which connects to the Galileo board.
Hopefully this will work! What do you think? Will I still be able to use a LCD shield and the pcie bluetooth card even at such a low power? Please respond!
007