I say, and with Allah's success: If someone fears missing the Eid prayer due to being busy with ablution and washing, it is permissible for him to perform tayammum and begin the prayer; because it is missed without an alternative, as it cannot be performed individually. Even if he starts the prayer while in a state of ablution and then becomes ritually impure, and fears that if he goes to perform ablution he will miss the prayer, it is permissible for him to perform tayammum; because the fear of missing it remains; since it is a busy day, he might encounter something that invalidates his prayer. Likewise, if he begins the Eid prayer with tayammum and then becomes ritually impure, it is permissible for him to perform tayammum to continue. Refer to: Fath al-Bab al-'Inayah 1: 167, and al-Durr al-Mukhtar 1: 162, and Allah knows best.