Is the intention to make up a fast flawed after hesitating for a few moments about completing the fast due to burping and feeling heartburn after the dawn adhan, then deciding to complete the fast as a supererogatory one before it became clear that this does not break the fast?

Your intention shifted from making up a missed fast (qada') to a supererogatory fast (nafl). However, the make-up fast is still valid and is not invalidated by the change of intention. This is the view adopted by some scholars, such as the Hanafis and the more authoritative opinion among the Shafi'is.