Bring about 1 inch of water to a boil in a large saucepan fitted with a steamer basket. Add squash, cover and steam until very tender, about 15 minutes. Drain and return to the pan. Add 1 1/2 teaspoons chile powder and salt. Mash until mostly smooth; cover to keep warm.
Meanwhile, combine beans, scallions, 2 tablespoons lime juice, 1 tablespoon oil, cumin and the remaining 1/2 teaspoon chile powder in a medium bowl. Toss lettuce with the remaining 1 tablespoon each lime juice and oil in another bowl.
Spread about 1/4 cup squash on each tostada. Top each with about 3 tablespoons of the bean mixture, 1/4 cup lettuce and 1 tablespoon cheese. Sprinkle with pepitas.