How can one reconcile the Hadith that describes people whose good deeds are like mountains, yet Allah makes them scattered dust because when they are alone with Allah's prohibitions, they violate them, with the Hadith, "All of my Ummah are forgiven except for the Al-Mujahirin (those who make their sins public)"?

There is no contradiction between the two hadiths, for both encourage compliance with Allah's commands, avoidance of His prohibitions, sincerity in actions, and awareness of His constant watchfulness. The first hadith (definition) addresses hypocrites, dissemblers, or those whose bad deeds outweigh their good ones, for Allah does not invalidate anyone's good deeds without cause, and faith and sincerity are conditions for the acceptance of deeds. As for the second hadith, it means that the servant remains within Allah's pardon as long as he does not openly commit sin and disregard religious commands.