Is it permissible to distribute the making up of missed prayers due to menstruation over several days, if waiting for a day or two to confirm purity causes hardship, difficulty, and depression, affects devotion, and increases obsessive thoughts, such that the prayers of the day of purity are made up on subsequent days?

What you are doing by waiting after seeing purity (tahara) is an impermissible mistake. Your duty is to perform ghusl (definition) and pray immediately upon seeing purity, indicated by one of its two signs (dryness or white discharge). If blood returns after that, you are in menses, unless the total days of bleeding and the intervening period of purity exceed fifteen days. As for istizhar (waiting to confirm purity) according to the Malikis, it applies if the blood exceeds the customary period, in which case the woman observes three additional days as menses. You must make up the prayers you missed after seeing purity and before performing ghusl, and repent for your negligence in learning matters of your religion. As for waswasah (obsessive whispering), its cure is to disregard and ignore it.