Using the two-digit numbers as octal indices into the alphabet, the shortest path from START to END (L, L, L) spells out "ALDES", which is unenlightening. If we start instead by taking the right-hand path out of the START edge, we get "ACINGSIDES" (via R, R, L, L, L, R, L), which at least ends with the word "SIDES" and is therefore beginning to get interesting. Try taking this path from START:
L, R, L, R, L, R, R, R, L, L, L, R, L
This path loops back to the START edge after five steps, and then picks up the previous path all the way to END, yielding the message "ALIGN FACING SIDES".