Is it permissible to fast the six days of Shawwal before making up the missed six days of Ramadan?

Your voluntary fasting of the six days of Shawwal before making up for the days you missed in Ramadan is valid and beyond reproach. This is the preponderant opinion among scholars and the madhhab of the majority, with the caveat that some scholars stipulated that the virtue mentioned in the hadith is only attained by one who has fasted the entirety of Ramadan.