Alternatives for other growing zones, or based on availability:
For sunchoke alternatives, some people have access to yams, especially the ones that give "air potatoes" in the fall. They are perennial, getting bigger with age and spread by edible air potatoes (a little too easily if you have neighbors who don't want free food). David the Good has some articles on his website about which ones are good for eating.
Where I grow we get more heat than cold; kale would be the crop that gets babied with a short harvest window. Horseradish grows well here and even the leaves are medicinal; they do better than kale for me with bugs and harvest window and neglect. For summer we use lamb's quarter; it's related to spinach, grows early spring to early winter in the heat, and is SUPER "weedy" (ie spreads easily, no care required, pest and critter resistant). You can also use care-free trees that grow in your area to make salads or a leaf concentrate (see Leaf for Life website). Some, like mulberry, will provide a crop of berries as well as leaves and you can totally defoliate them and they'll come right back in 2 months, with more berries!
I also have wild garlic because the walking and potato onions I bought died on me but the foraged garlic is thriving under neglect! The greens are mostly only available in the spring but the bulbs are always there, and they, too, are "weedy", spreading and thriving.
By your definition they wouldn't count as food pumps, but if you're around for it foraging nuts & acorns is also a viable strategy for cheap and easy calories. Acorns require processing; but you can get upwards of 200# per oak tree and the processing can be done with minimal equipment and hands-on time so I think it's still worth eating if you've got it.