Test that all 4 empty squash halves fit cut-side up in a 6- to 7-quart oval slow cooker with the lid closed; trim a thin piece from an outer curve if needed to steady them. Remove while making the filling.
Bring quinoa and 1 1/2 cups water to a boil in a covered saucepan, reduce to low and simmer for 15 minutes. Rest covered for 5 minutes, then fluff.
Mix cooked quinoa with beans, corn, pepper, salsa, cumin and salt. Brush squash flesh with oil and divide filling among the 4 cavities, mounding any extra over the cut surfaces.
Pour 1/2 cup water into the slow cooker and arrange filled halves cut-side up. Cover and cook on high for 3 to 4 hours until a knife slips easily into the squash flesh.
Sprinkle cheddar evenly over the halves, cover and cook for 5 minutes more until melted.
Lift each half with a wide spatula and serve one per portion, leaving cooking water in the crock.