There's no question that hydrocarbon storage of energy is way lighter than battery technology, cf. Wikipedia's Energy density; in energy storage and fuels.
Carbohydrates + dynamo
So I wonder why, with modern rare earth magnetic materials you would say that:
...and dynamos are probably not feasible.
Get a high conversion efficiency hand (or foot) cranked generator. Bring and eat extra carbs, train accordingly ahead of time to build the appropriate muscles to make enough power each day.
Walmart has them so I would expect there are better ones as well. This is one candidate.
Fuel Cells (hydrocarbon, not hydrogen)
Yes this is an exotic solution, but maybe you can bargain for a sponsorship unless it's against the rules.
Someday we'll be charging our laptops with lighter fluid, but there might be something available today.
While hydrogen requires heavy tanks and is tricky to handle (it leaks due to tiny molecules with high mobility) light hydrocarbons like methanol or possibly propate/butane may be available.
Here is an example of the technology, but I think this particular model is not suitable for your application.
The Honey Badger 50™ reformed methanol fuel cell is the industry’s newest ultra compact and highly portable fuel cell. The Honey Badger 50™ is designed for rugged, off-grid uses.
The Honey Badger 50™ is ideal for a wide variety of higher power electronic applications, including radio and satellite communication gear, remote and mobile surveillance systems, and laptop computer and battery charging.
A plot of selected energy densities (excluding oxidizers). Date: 22 December 2008 Source
