The Good Friday liturgy, which is not a Mass but includes the reading of St. John's Passion, prolix General Intercessions, the Veneration of the Cross and Divine Reproaches, Communion, and then the Stripping of the Altar, must be presided over by a priest or deacon as per the United States Conference of Catholic Bishops and the Roman missal (http://www.usccb.org/liturgy/goodfriday.shtml).
This is but the latest liturgical experiment at Our Lady of the Angels, one of the most innovative parishes in the Archdiocese of Anchorage. Past liturgies have included homilies given by nuns and lay women, a 'choral performance' of the seven readings at Easter Vigil, and dances by middle-aged women in full-body leotards.
Not all parishioners enjoy the creativity, however. Numerous families will be forced to travel outside of the Kenai Peninsula - an area roughly the size of West Virginia - to find a priest or deacon interested in celebrating Mass according to the rubrics.
The Archdiocese of Anchorage has not yet released a statement concerning experimental liturgy. However, the Second Vatican Council had this to say:
Therefore no other person, even if he be a priest, may add, remove, or change anything in the liturgy on his own authority. (Sacrosanctum Concilium, ¶22, §3)