From here you can either (i) head right to start the entire puzzle again and rejoin the path in the midst of the spike traps (step 1 in the instructions above), or (ii) head left via a pair of Veteran Cave Spiders to skip the gargoyle flame traps (step 6 in the instructions above).
Note that although there seems to be a safe spot in the middle (between the second and third heads), this is not the case, and the traps will continuously hit you there. These hit for a 33% of your health per pulse and apply burning.