Use a knight to restrict the king before the rook checks.
A knight covers the king’s escapes while a rook or queen checks along an edge file. The king’s own pawn or piece can block another escape. Prepare the knight’s control before opening the checking line.
Sacrifice your knight to continue the attack
If the pawn takes your knight, your pawn can give check. In this continuation, your pieces keep attacking and give checkmate.
2 more clean runs (at any point) to reach Recall.