With that many people you are going to have a challenge feeding them all. Even chicken and rabbits would strain the capabilities.
What “other” food sources are around?
Squab? Four and twenty blackbirds baked in a pie”? Nutria, muskrats, frogs? Even fish will likely become scarce as people reduce the breeding stock. Aquaponics?
Being in an HOA means that you are close enough for the neighbors to see you putting out traps and nets, you risk losing the food as well as the gear.
Sorry no real answers only questions but ask the right questions and the answer should present itself.