Is it permissible to read from the Mus'haf and distribute a complete recitation (khatmah) in all supererogatory prayers, and not only during Qiyam al-Layl and Tarawih?

It is permissible to read the Quran from the Mushaf in supererogatory prayers (Nafl), absolutely, such as during Qiyam al-Layl (night vigil prayer) and other similar prayers. It is also permissible to divide the recitation of the entire Quran (khatm) among several supererogatory prayers. Reciting the Quran during prayer is better than reciting it outside of prayer. The best recitation outside of prayer is the recitation at night, especially during its latter half.