I don't see an AC outlet or way to charge a laptop with the device you linked. It would make a good backup phone charger. Something similar to that could be a viable solution.

We already have this Duracell Power Pack which we wouldn't mind using, but it can take a long time to recharge 15+ hours and we won't always be near an electrical source.

Would rigging a solar panel to a trailer be a viable solution? Would this generate a reasonable amount of power to keep things charged each day? (minus cloudy days of course)

It's a bit overboard, but if you have a big enough festy crew try to buy one of these. Paired with a solar panel, you'll have power for the whole weekend (and then some)!