The main thing that helps AM reception is bigger antennas. Try one of these: http://selectatenna.com - obviously it's not so portable though. With a moving receiver you're generally better off with FM because of AM fading like you describe.

The crank radios I'm familiar with have a rechargeable battery inside that's subject to failure and leaking just like any other battery. The crank simply charges it up. I don't know if the Freeplay works like that. It sounds like it might not, if the internal spring is generating power directly without a battery. That's more mechanically complex though, and may require more maintenance.