- one charge should last
how long?
I'd go with rechargeable battery pack & switching regulator to make 5V, small linear from there for 3.3V.
You can find higher voltage LiPos with charge control built in. I have one at home.
Here's one with a solar charger built in even:
There's a bunch of 14.8V packs here
http://www.all-battery.com/li-polyerbatterypacks.aspx
So the stuff is out there, you just need to look more.
The other option is a high capacity (mAH) 3.7V cell with boost regulators for the higher voltages: