Is melodizing the Adhan considered unlawful, and is feeling ostentatious when desiring to lead people in prayer a sign of ostentation itself?

Repentance erases what precedes it, and Allah replaces bad deeds with good ones. It appears that aspiring to and loving the imamate is permissible, for one with high ambition seeks a high rank. However, a person should not seek something they do not deserve.

If the Imam is absent, the one most knowledgeable of the Book of Allah and most learned in the jurisprudence and rulings of prayer should step forward to lead the prayer. If there is no one among the people more deserving of the imamate than you, and your prayer is sound, then you may step forward to lead. What is required of you is to seek Allah's help and to gain a deep understanding of His religion by seeking beneficial knowledge, memorizing His Book, and perfecting its recitation. Then, if you are needed for the imamate, you will be worthy of it.

Beware of aspiring to the imamate out of a desire for pride and superiority over people, for that is among the greatest destructive acts. Seeking knowledge and memorizing the Quran are pure acts of worship that should not be intended for anyone other than Allah. If you correct your intention and strive against your whims, and if Satan whispers to you, seek refuge in Allah from him and say: "O Allah, I seek refuge in You from associating anything with You knowingly, and I seek Your forgiveness for that which I do not know." Continue with your righteous deeds and do not abandon them.