Something to be considered is the legal ramifications of walking around in public with a loaded long gun. In most places (even without a martial law declaration) you are going to be running afoul of the law. This means that an otherwise chance, casual encounter with a rescuer/peacekeeper could go badly for you from (at least) a legal perspective.

You don't mention the area in which you reside but most states in the US allow for legal open or concealed carry of a handgun. I would much rather be legally armed with a handgun than illegally carrying a shotgun.

In a Katrina type situation like you propose I can think of very few reasons that I would want to leave my place of refuge if the surrounding environment is so hostile that the open carry of a long gun is necessary. Were something like this to happen in my local I know how I would proceed but my local laws may be dramatically different than yours.