The True Location of Chapter 21 in the Book of Samuel

Chapter 21 of the Book of Samuel seems very nonsequitor, so I will try to reconcile it with its context over the next several posts.  First off, the chapter starts off with a famine due to what Shaul had done to the Givonim (Gibeonites,) the resident alien Canaanite workers in the Temple who, as non-citizens, had no legal recourse.  Why wait until after David had dealt with his sin with Bat Sheva and all of the wars and revolts to deal with this seemingly trivial matter?  Rather, it seems reasonable that this happened immediately after David assumed power.  This is evinced by the fact the Givonim demand seven of the sons of Shaul, whom David delivers to them.  Earlier in the Book of Samuel, we see David asking if Shaul had surviving sons, so that would clearly have to have happened after the incident with the Givonim.