With 15 titles over the past decade, Kikkan Randall has turned the U.S. National Championships into something of a one-woman show. In the 2010 edition, which was held in her hometown of Anchorage, she swept all four events—collecting nearly $5,000 en route to wins in two distance races and a pair of sprints. This year, the country’s fastest women will assemble at Black Mountain in Rumford, ME. But when the first event of the championships...