Is there an alternate way to organize items on a shelf other than drag and drop? I find my icons sometimes moved (usually to the left of a shelf), and the drag/drop operation doesn't always work so well. Dragging sometimes opens a spot for something to be dropped, but not always. And you can't drop on top of another icon to say "place this icon here."

Nope, drag & drop is 'all' you get. On the other hand, even if the shelf does not open the insertion point (just wiggle the mouse a bit, it should work) you can always drop into the gap between two icons - as long as you don't drop into an actual icon, it will work.