Is it permissible to delay the Dhuhr prayer past its prescribed time due to fear of being late for school and the harm that would result, especially given the high quality of education at this school and the difficulty of transferring elsewhere?

The Dhuhr prayer, like other prayers, has a starting time before which it cannot be performed, and an ending time beyond which it is not permissible to delay it, except when combined with Asr. If the Dhuhr prayer is performed before its time, it is not valid. If you fear genuine harm, you are permitted to combine Dhuhr with Asr by delaying Dhuhr (Jam' Takhir).