The best way to fix this error is to replace all the thin-walled solids with midsurface geometry and mesh with shell elements instead of solid elements.  When you do that, the shell element local coordinate system will no longer line up with the global axis as it does for the solid elements.

Another way to fix this error is to slice all the thin-walled solids up so that you can sweep elements through the thickness.

You didn't answer my question: What direction does the grain of the wood run on the surface that is deforming excessively?