Is it obligatory to make up the Dhuhr and Asr prayers as a precaution due to the possibility of purification before the Maghrib call to prayer, in the event that one is not certain of purity until after midnight and has made up the Maghrib and Isha prayers?

There is no obligation to make up the Dhuhr and Asr prayers in the situation mentioned. The original state is the continuation of menstruation, and this certainty is not removed by mere doubt. If there is doubt about the cessation of menstruation before Fajr, then there is no obligation to make up the night prayer until it is confirmed that it ceased before Fajr with enough time for purification and prayer.