To put it more succinctly, the immutable numbers are the 3648 x 2736 pixel numbers. The 72 and 180 dpi numbers are scaling or mapping numbers.

If you change the former, you have altered the picture. If you alter the latter, you've really not done much of anything.

The idea is that pixels have no defined physical dimensions. By applying a DPI or PPI mapping to them, you can establish dimensions.

At best, though, they're suggestions. But since your pictures don't have any logical pixel-to-inch mapping (for example, in your panoramic photo, there's a column that occupies many more pixels than a palm tree just above it, and that palm tree occupies more pixels than a five-story building somewhat farther above), the only thing that they can indicate is how large to print out the image, and you're going to ignore that anyway.