I played around with this in rhino 5. i projected your curves onto 3 planes. then made new 3d curves using curve from 2 views. i then made the surfaces. when i try adding the beam you speak of, it doesn't make sense. the curves from 2 views don't intersect the surface you defined. basically it seems like the beam is over constraining the situation. not really sure what to do with it. i attached a file you can look at.