hi egon,
I'm not so familiar with matrix transformation, but I did try using obj export method in Blender's source code (global matrix * object rotation matrix), where global matrix is the destination matrix which represent JPCT coordinate system and object rotation matrix obtained from Blender API. Yet, no luck on that. I wonder if you can show few guidance on the matrix tranformation, perhaps the one you mentioned, mirror transformation, or other keyword to look for in google.