Jenks,

Maybe the parable of the fishes and loaves works best here. You might want to contribute your spare stuff as the starting point for a central store of goods that could be drawn upon in the event of major event. Have your neighbors contribute to the stores a little bit at time, an extra pack of TP or canned soup or dry milk, etc. Have a defined list of needed items so you don't get the junk people have lying around.

Now, if the logistics of that get out of hand (and it may quickly put a burden on the organizers) instead create a emergency supplies phone chain (or walkie-talkie chain as Blast suggested)so that after an event you could organize an inventory of stuff on hand and also gather information on who needs what. A central spot to take in supplies from those who have for those who don't.

In your situation this might be workable, since everyone there is known by someone else and "outsiders" might not be able to mess up the communal effort.

Obviously this idea isn't simple to plan or execute but given the nature of your community might be a good fit.
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In a crisis one does not rise to one's level of expectations but rather falls to one's level of training.