Drunkard's Walk

After a night of celebrating, our hero leaves r1c1, through the fog, trying to get home to r9c9. With each step, they move to an orthogonally adjacent cell, forming a modular line as they go. (That means any set of three contiguous digits along their path must include one each from {147}, {258}, and {369}.) They stagger from streetlamp to streetlamp along the way, each indicated by a yellow disk in a cell. Some of the street lamps are visible from the start but others are hidden by the fog and will only be revealed when correct digits are placed nearby. Their path must lead them to every streetlamp. All streetlamps are from the same modular set and whenever a number from that set is on the path, it appears as a street lamp. Numbers from that modular set which are not on the path are not streetlamps. If our hero enters a killer cage, they must completely traverse the cage before exiting it. Some killer cages may be avoided entirely.