... And you may be right, but I still tend to think it's a bit more complicated than that.

Another explanation that would still fit with your idea is that the DO has more influence (read "visibility", in this case) over places in the Pattern nearer SG than farther away, and THAT is why his ability to capture souls is a function of distance from SG, rather than it being because he has to search more and more threads as the distance from SG increases (implying that his search pattern radiates out from SG).

Since we're dealing with a god here, I tend to prefer explanations that are more metaphysical than physical.