It's interesting that if you run this system with the PCs playing themselves you're vulnerable to the local culture or context. For instance I'm from the UK. We don't just guns lying around all over the place!
Should make arming the party that much more challenging. Or what about people playing in more rural or isolated areas? They've got far less to work with, but might have reprieve from the immediate effects of the apocalypse? More time to react/prepare?
Seems a really interesting setting. Could be very challenging on a personal level too. I might have to role play that my partner and our children are either dead or undead etc.