I don’t think it is a simple perspective divide that you’re looking for. You want to switch the frustum to a reverse or Byzantine frustum. This is far harder to achieve with the OpenGL view frustum.
If you do end up computing the projection matrix yourself, vtkCamera allows using externally provided projection matrix directly. See vtkCamera::SetExplicitProjectionTransformMatrix and vtkCamera::SetUseExplicitProjectionTransformMatrix