It seems that there are two situations that can apply to the Intersecting Cell in a kitebox: one in which the two strings cross over eachother at that point, and the other case where it is not crossed over but is in line with the two strings, or is common to the column and row that your strings are assembled in.
Another thought. Leren indicated that he prefered looking for kites by finding the possible strings first. Does that allow you to scan for kites and syscrapers at the same time, as they have some of the same features?
Yogi