Usually people who need it have hardware cockpits and only need the image of the outside world; this was done initially for these cases. If you want to have a 3D in-game cockpit rendered with the current version, you'd have to have it finely tesselated. The problem is that cylindrical/spherical projections are curved. When you project a triangle that's close to the camera, the triangle endpoints (vertices) are projected correctly, but the pixels inside are interpolated linearly, because hw rasterizers can't work otherwise. The error is progressively larger as the pixels are further away from the nearest vertex.
If you want to minimize the error, you must break all triangles that would end up covering larger parts of the screen into smaller ones. That can be done automatically (on modern GPUs), or manually by tesselating the cockpit finely, avoiding any long triangle edges.
The models we have got there aren't tesselated enough, there are some long triangles on the sides, and that completely breaks the projection. Once the auto-tesselation is implemented, it should handle these cases.