I use the BTZS, so the metering is done with an incident meter. Theorethically this averages the light in the dark zone and if you have done the testing you get the correct exposure for the dark tones.
When I was using the ZS I found that placing the shadows with detail on zone III always resulted in underexposed negatives, I usually placed my dark zones with detail in zone IV and this seemed to work.
The print has detail on the left side, you can clearly see the wall and the rock, but it goes to dark with no detail in the lower left and right hand corners.

I would suggest you place your shadows in zone IV, it worked for me, it might work for you.