CHICAGO—Chuck Baum gently tapped the wheels on a miniature race car with a sleek, white-and-blue body that he had shaped over 10 hours from a block of wood.

He had won three races with his pinewood cars—long the drag-racing vehicles favored by Cub Scouts—at an event the night before. As he awaited the start of another race on a recent Saturday, he was excited but uncertain.

"I...