Is it permissible for me to seek to lead prayers (Imamah) in a Sunni mosque, given that I possess good Tajwid (recitation of the Quran) but do not have the entire Quran memorized, whereas their current imams have memorized the entire Quran but their recitation contains subtle errors (Lahn)?

You are not entitled to request to lead the prayers for two reasons: First, there are those among them who have a better memorization of the Quran than you, and the hidden لحن (intonation error) does not affect the validity of his recitation. Second, the regular Imam has a greater right to lead the prayer, even if someone else is a better reciter than him. We advise you to focus on seeking beneficial knowledge and acting upon it, and to abandon the pursuit of imamate.