Bruce Barnbaum makes a strong case for placing the shadows on Zone IV.
John Sexton does the same. Look at both gentlemen's pictures and you don't need much more to be convinced. On the other hand, learning to visualize a Zone III also helps. Zone III is much darker than many people realize. It is a dark shadow with texture, not a shadow with full detail. If a shadow with full detail is easier to visualize for you, placing shadows on Zone IV is the right thing to do. Whatever it takes to gives shadows plenty of exposure!