Is a person considered to be righteous, and is it permissible for him to continue leading people in prayer in the absence of the Imam, if he has memorized parts of the Quran and is confident in the pillars of prayer, but feels a lack of complete heartfelt devotion, despite his conviction that working for people is not hypocrisy, and his eagerness to recite Surah Al-Baqarah daily to ward off hypocrisy?

It is permissible to continue leading the prayer in the absence of the Imam. Humility (khushu') is not among the obligations of prayer or the conditions for Imamate, but tranquility (ṭumaʾnīnah) is one of the pillars of prayer. If there is someone among the worshippers who is more entitled to lead the prayer, then it is preferable to put him forward.

Regarding your statement, "I do not fear showing off (riyaa')," if you mean that you do not abandon good deeds for the sake of people, then this is commendable. However, feeling secure from riyaa' might be an illusion or conceit, as it is one of the most dangerous and very subtle diseases of the heart. The Prophet (peace be upon him) said: "O people, beware of this shirk, for it is more subtle than the creeping of an ant." The remedy for this is through supplication and reciting the Qur'an.