This is the external battery I used during a recent vacation. $30 and it holds enough juice to recharge a recent iPhone about 5-6 times. (It has 13 times the capacity of the Mophie you linked to.) There are cheaper options as well that still offer decent capacity (compare prices on a $ per mAh basis).
However, I do think the appropriately Mustachian answer to this is: you're camping. Do you really need a smartphone during a camping trip for anything other than emergencies or maybe a once-a-day check-in with someone back home? If that's the case, just keep it powered off 95% of the time and you shouldn't need any external power source to last a week.
Also, if the cars are going to be near your campsite, you may be able to charge from them even when the car isn't running. Recharging an iPhone won't put you at risk of killing the car battery.