Is it permissible to supplicate with: "O Allah, I ask You by the Torah which You revealed to Moses, and the Gospel which You revealed to Jesus, and the Qur'an which You revealed to Muhammad, may Allah’s prayers and peace be upon him, to do such and such"?

There is no impediment to interceding with Allah Almighty and supplicating to Him through His Books that He revealed to His Prophets, for they are His speech and an attribute of His attributes. They contain many of His Most Beautiful Names and Exalted Attributes, by which the Exalted commanded us to supplicate to Him, and supplicating by them is legislated.