You will need to save the model and transformation data in your application differently than they are stored in the file. In general, it sounds like what you need to do is:
- Load the FBX
- Apply the transformations to each part according to the FBX
- Apply the transformation to invert the Z-axis on all of the vertices
- Render/use the resulting model.
Applying the FBX transformations in the wrong coordinate systems will yield incorrect results.