I wonder why earlier pings don't deserve much attention. They could at least tell us whether it is the northern arc or the southern one which should be taken into consideration.
Well, no. Assuming only Inmarsat picks up the ping - reasonable if the plane continues generally westward - you have no cross reference. Just an angle.
All that does if give you another set of arcs with a slightly different radius.
The key point is that the arcs we see from the last ping position go right over the last radar position, which means that the airliner very likely took a course roughly corresponding to one of those arcs.
Earlier signals could indicate whether the plane might have "cut the corner", which would be reasonable to assume if it flew a straight course.
All we can now from the arcs is that the plane is now on the surface of the planet up to a half hour's flying distance from the arcs.
That's a huge area, the size of a large country.