Why not reach back to older breeds that used to be raised for meat. I am raising Dorkings (there are many others) for this purpose - they go broody reliably so they will resupply you without much work on your part.
You would not need "breeds". You would need chickens that can mostly feed themselves during the good weather months. And to an extent in the bad winter months depending on how rough your winters are. People all over the world still do that. My parents and grandparents did but that was a long time ago. They raised a landrace chicken, fairly small, could fly pretty well, went broody and raised their own replacements, and were well-suited to survive in that climate and in those conditions. And they knew how to cook them so a small chicken could feed a large family.
I'm not arguing with you about Dorkings or any other breed. As long as they meet your requirements they are a great place to start. But the traits I'd be breeding for would be the traits that would make them suitable to survive rather than the traits that make them a breed. In my opinion breeds developed when people were affluent enough to develop them. Until then, people were breeding chickens to meet the human's needs.
Basically in case the world goes to heck we can produce our own. We know we can eat regular ones but it's just easier.
I'd disagree that Cornish Cross would be easier, not if you have to pamper them and you would. What could be easier than having a chicken that can feed itself and take cares of itself. All you have to do is feed it if the weather is that rough for an extended period of time and protect it from predators. That's why for thousands of years farmers and peasants have been raising the landrace chickens that can take care of themselves. They have enough other things to do to survive than spend time taking care of chickens.
I'd argue that the eggs would be more important than the meat from chickens. Eggs have great nutrition. Even if your chickens only lay 80 to 100 eggs a year, since they feed themselves keep more chickens so you have enough eggs. Besides, once Cornish Cross reach butcher age you have to butcher them, otherwise they die on you. How are you going to preserve the meat for later? With dual purpose type landrace chickens butcher then when you are going to eat them. You just have to know how to cook them.
It can be fun to fanaticize about an end-of-the-world scenario. I know I can be a killjoy sometimes. If I've upset your fantasy world by interjecting a little realism I apologize.
Modern power, water, sanitation - where breakdown of those systems will quickly overwhelm any individual effort to counter.
In that scenario my first efforts would include securing a safe water supply. Without safe water you are unlikely to survive long.
To me, fire can be used to cook, heat you in winter, and provide light. That's what people did before electricity was common. I used an outhouse until I graduated high school. Our water came from a cistern but if it did not rain for a while we used water from a hand-dug well at the foot of the hill. Since the well water was cleaner we hand-carried well water for her when she needed to do laundry.
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