From my understanding,
Yellow line closes after stop 6; red line closes after stop 12; pink line closes after stop 18; and rose line closes after stop 42.
Could you do:
Yellow line to Ikebukuro (3 stops) plus an additional stop to transfer and switch to the Red line (12 stop). Then go to M21 Hongo-sanchome (4 stops) and transfer and switch to the pink line (12 stop). Then go to E11 A17 Kuramae (3 stops) and transfer and switch to the rose line (12 stop). Then go to A1 Nishi-magome (16 stops).
Altogether that seems to take
2932 stops, if I've counted correctly.
Is this reasoning correct?