Minecraft: 1.12.2
Forge: 2705
Storage Drawers: 5.3.7
Packing Tape: 0.7.6

Note: I am using your packing tape, rather than SD's.

So, I moved some storage drawers downward and placed them from the other side of the wall. Reading your CurseForge page, I also tried placing them while sneaking, and unwrapping them while sneaking. In all cases, they reappeared in their original orientation, despite that I was facing the opposite way when placing them.