Archeocook is a great neologism and a really interesting concept, and I think you've done a great job executing it as a simple and relaxing narrative experience! I was excited to play this after reading your artistic statement, as I sympathise greatly with your frustration at the narrowness of the "apocalypse" genre, it's oft un-noticed western parochialism, and the disappointing inability to imagine a world outside of the confines of capitalism. I think your resulting effort to focus on the mundane lives of people rebuilding their (non-temperate!) world really pays off and helps to bring some of these themes to life.
As it currently stands, I agree that you have a solid worldbuilding base moulded into a polished short story, which is releasable as such as is. I do hope, though, that you keep tinkering away, as I'd love to play a longer version with some simple puzzle/card mechanics like you suggest in your release plan. Also, I love Le Guin, and myself and my partner for this jam both loved Pentiment, so I think your influences are very well chosen!