How about a Twitter client that in a non-internet situation can just share locally and then when anyone gets internet access it auto-pushes the tweets out. Logistics / permissions are complicated I realize, but a 'layer' on top of Twitter would be ideal.
Or build a website that can account for geographical data, sending you only relatively close peoples messages in order 'store' and potentially transmit only the ones that are important.
The thing here is to have three or four really good fall back ways of sharing, overall I thing it's a really neat idea, and I'll start using it and sharing the concept/code as much as I can :)