Interesting questions. Gadsden did negotiate the purchase of the Mesilla strip--the section of present-day NM, AZ, and CA south of the Gila River. He wanted to secure more. At one point, he even attempted to purchase Sonora and Chihuahua for the US.
His plan for cartas de seguridad related to the citizenship status of former slaves in Mexico. Why was he so intent on convincing the Mexican government to deny their citizenship, forcing them to use the cartas de seguridad instead?