Is it permissible to change the intention of fasting the days of Shawwal from reward to make up (for missed fasts) after having fasted them, this being after learning that making up for Ramadan (fasts) takes precedence?

The days fasted by the questioner are not sufficient to fulfill the make-up fast of Ramadan, because it is a condition to have the intention for making up Ramadan's fast before the true dawn, and changing the intention is not permissible. Fasting the six days of Shawwal is valid before making up Ramadan's fast, and the make-up of Ramadan remains an obligation.