Is it permissible to remind oneself with "Allah is looking at me" before reciting Al-Fatiha, Tasbeeh, and Tashahhud in order to attain khushu' (devotion/humility) in prayer?

What you are doing is good and helps in achieving khushu' (devotional humility) in prayer. Therefore, a Muslim should feel that every act of worship performed brings them closer to Allah, and that Allah is watching them and observing them while they perform it, and that they might die after finishing it. This motivates them to improve and perfect their worship, in accordance with the Prophet's (peace and blessings be upon him) saying regarding Ihsan (excellence in worship): "To worship Allah as if you see Him, for if you do not see Him, He surely sees you."