Mmh, you can move your source point farther away from the layer generating the shine, but that will also make more adjustments necessary because rays will get "thinner". Surely this can be automated with expressions. What exactly are you trying to do?
Rays in Shine have a fixed spread - that is to say the virtual source point is a fixed distance in z-space from the object which radiates. I would like to manipulate the angle of the cone of these rays. So when you say you can move the source point farther away from the object generating the shine, how would you do this, given that the source point has only x and y controls?
You are right in describing the spread as fixed, however, as with sunlight, they become (seemingly) more straight the further away you move from the source. This can be achieved by using AE's interpolation methods in expressions. So assuming, you create a dummy Z-depth object the distance of it form the other layer could be used to manipulate values in Shine. Most notably you would have to work with light boost and ray length. Other than that, you cannot manipulate the ray angel directly, but you may want to look into other techniques for that. I've done a few of those trickeries using the corner pin effect to e.g. distort a extremely stretched fractal noise. All you need to do is think it thru and create your mattes accordingly.