Last fall New York Gov. Andrew Cuomo expressed dissatisfaction to Metropolitan Transportation Authority executives with the cleanliness of their two road tunnels. His discontent sent MTA officials scrambling to devise a plan to more thoroughly wash the tubes.

“As we can agree the Gov has decided that tunnel appearance is important,” Cedrick Fulton, the head of MTA Bridges and Tunnels, wrote to colleagues in a Nov. 15 email. Mr. Fulton laid out a strategy in the email to intensify washing of the Queens-Midtown Tunnel and the...