What is the ruling on the muezzin praying over the deceased before the Imam prays over it, out of a desire for the reward of a Qirat, knowing that if he were to go after the prayer, he might miss the funeral prayer?

The Sunnah (definition) for the funeral prayer is to perform it in congregation, and the larger the gathering, the better. It is permissible to pray it individually, and it is permissible to pray it before the Imam leads the prayer, if it is difficult to join the congregational prayer, or at the graveyard before burial. There is no harm in praying it individually in this situation.