Is saying "Astaghfirullah Al-Atheem" (I seek forgiveness from Allah, the Mighty) between the two prostrations sufficient instead of "Rabbighfirli warhamni wa'fu anni" (My Lord, forgive me, have mercy on me, and pardon me)?

The established supplication between the two prostrations is what was mentioned in Fatwa no. 32290. As for saying "Astaghfirullah al-Azim (I seek forgiveness from Allah, the Almighty)," it is not established between the two prostrations. Therefore, one must limit oneself to the established supplication only.