Is there an order of priority for who should step forward to fill a gap in the first row of congregational prayer, or does everyone have the right to do so?

There is no specific designation in the texts regarding who should be the first to fill a gap in the row. However, the general wording in the texts indicates an encouragement for every worshiper to hasten to close it. The person closest to the gap may be more deserving because they do not require much movement. If the person closest does not step forward, then others should.