Is it permissible to work long hours at night in a way that affects the performance of prayers at their prescribed times, while experiencing distress and an inability to change the nature of the work schedule or leave the job?

Initiating the prayer at the beginning of its prescribed time is better, based on the hadith (definition): "Prayer at its [appointed] time." However, it is permissible to perform it at the end of its time before it expires, based on the hadith of Jibreel: "The time is between these two times." So, if you pray Dhuhr or Maghrib at the end of their times before the entry of the next prayer's time, there is no sin upon you as long as you performed the prayer within its time. The time for Maghrib ends with the disappearance of the red twilight. Your diligence in waking up for prayer at the beginning of its time is better and further safeguards against the prayer going beyond its prescribed time.