Is it permissible for me to recite these detailed supplications while the Imam is reciting Surat Al-Fatiha during a loud congregational prayer?

Scholars have differed on the ruling of making supplications (du'a) when reaching verses of mercy and punishment, and making requests during prayer. The Shafi'is consider it recommended in both obligatory (fard) and supererogatory (nafl) prayers, citing the hadith of Hudhayfah as evidence. As for the Hanbalis, they recommend it only in supererogatory prayers, believing it is not recommended in obligatory prayers because it has not been transmitted from the Prophet (peace be upon him) for the latter. Meanwhile, the Malikis consider it disliked to make supplications at this point in obligatory prayers. The summary is to abandon this supplication at this point, especially since it is a lengthy supplication that might distract from listening to the recitation, and because it has not been transmitted from the Prophet (peace be upon him) in obligatory prayers.