Put the chiles in a bowl and cover with the boiling water. Soak until they are soft and pliable, 15 to 20 minutes. Drain and discard the stem, seeds, and tough skin; chop the chiles.
Put the oil in a large pot over medium-high heat. When it’s hot, add the chiles, onion, and garlic and cook, stirring occasionally, until the onion softens, 3 to 5 minutes. Add the tomatoes and sprinkle with salt and pepper. Bring the mixture to a boil, then adjust the heat so it bubbles steadily. Cook, stirring occasionally, until the mixture has thickened, 15 to 20 minutes. Taste and adjust the seasoning, adding some or all of the sugar if you like; remove from the heat.
Combine the beans, avocados, scallions, cumin, cilantro, and lime juice in a medium bowl. Sprinkle with salt and pepper, then stir to combine; taste and adjust the seasoning.
Using an immersion blender, puree the tomato sauce right in the pot. (Or, working in batches, carefully transfer it to a blender or food processor and puree until smooth. Pour the sauce back into the pot.) Turn the heat to medium. Add the tortilla chips a handful at a time and stir gently to combine. Once all the chips are coated with sauce, divide the chilaquiles among 4 bowls, top with a spoonful of the black bean relish and serve right away.