Is it a condition for the validity of the Ibrahimiyyah prayer that it be recited in one of the narrated forms, or is it permissible to pray it using any other form?

It is not a condition for the validity of praying upon the Prophet (peace be upon him) to recite the Ibrahimiyyah prayer. Rather, it suffices to say: "Allahumma salli 'ala Muhammad (O Allah, send blessings upon Muhammad)," which is the minimum acceptable. However, the form that the Prophet (peace be upon him) taught his companions is more complete. Al-Nawawi mentioned that the minimum prayer is "Allahumma salli 'ala Muhammad," and that saying: "Allahumma salli 'ala al-Nabi (O Allah, send blessings upon the Prophet)" or "Allahumma salli 'ala Ahmad (O Allah, send blessings upon Ahmad)" is sufficient, as is "Sallallahu 'ala Rasulihi (May Allah send blessings upon His Messenger)." Al-Alusi stated that "Allahumma salli 'ala Muhammad" is sufficient because it is agreed upon in the narrations.