If I remember correctly I had similar issues in the past where the wheel bones are not direct children of root.
I deleted the armature and oriented the vehicle correctly then added a new armature, I only rotated the bones to get the proper X,Y, Z.
I assigned the vertex groups to each bone and exported the vehicle. I replace this car in the vehicle template and changed the bone names and physics asset and it worked as expected.
SK_Vehicle.fbx (712.3 KB)
Vehicle.blend (3.6 MB)
Let me know if you have any questions.