Use a voltage multiplier.
Also, look at the differences between a dynamo and a generator.
A dynamo is a generator, but a generator isn't necessarily a dynamo. In a certain context the terms are interchangeable, but a dynamo produces DC, where a generator can produce either DC or AC (in which case it's generally referred to as an alternator).
This looks fun
It does, but unfortunately it's meant for AC to DC (from what I've seen so far), it's similar to a rectifier except the added caps push a little higher voltage to the next caps, and so on. I'm not sure if DC would work since I think it needs the AC oscillation to push the voltage to the next stage. I'm envisioning a ram pump, but I could be entirely wrong.
I did find a a couple of voltage multiplier circuits that were DC to DC but they could only handle 600mA. I'll keep researching, maybe I can find a circuit for higher amperage use. One way or another my knowledge of electronics will improve.
Thanks for all the ideas. If you're not constantly learning or trying something new then you're not living right.