Seems a bit silly to try to setup such a complex sneaker net. Generally I'd expect hams to coordinate with local folks in person or with family radios (very common) and then use something like js8call. Even a modest ham setup (5-10 watt radio, a car battery or two, a spool of wire for an antenna, and a solar panel or 2) could network a neighborhood to different cities, states or even countries for 100s to 1000s of people a day.
js8call is a pretty amazing piece of technology. Crazy efficient encoding to allow sending at 20db or so UNDER the noise floor, allows a few watts to go 100s or 1000s of miles, and allows store/forward (in case the destination isn't online) as well as multi-hop routing.
I suspect there's more hams about than you think, 3M in the world, around 700,000 in the USA. So that's around 1 in 500 in the USA, and from what I can tell smaller/more remote communities are more likely than average to have a ham around. If a fire/storm/earthquake/landslide/power outage just head towards the center of town and check the parking lots for any churches, police stations, or town squares. Bring whatever text messages you want to send on a thumb drive in plain text. Said ham will likely know about the local emergency responses are, where the water truck will show up, and where whatever resources you need are available. In particular if you need any prescriptions make sure you know the brand name and drug name for any needed meds.