Coordinate two rooks near the enemy king.
Two rooks can work together close to the enemy king. One checks while the other protects it or takes away an escape square. Their protection matters more than merely reaching the seventh rank.
Sacrifice your queen to continue the attack
If the king takes your queen, your rook can give check. In this continuation, your pieces keep attacking and give checkmate.
2 more clean runs (at any point) to reach Recall.