Ahh - power up! Finaly have the system running on one of the two new monitors.
Comparing the favorites menu and the shelf. Initially the two were the same, with just a slightly different order. Now, however, the two are no longer the same.
Contrary to the appearance, the favorites menu is separate from the shelf. This is where the menu is edited.
Editing the shelf It was a bit of a trick to find where this was buried, much like finding where to edit the favorites menu.
Exiting the desktop is slightly hidden on a sub-menu. Possibly better to avoid selecting the item by mistake, but not necessarily intuitive either.
Sometime later, I finally got new monitor stands to put both monitors side-by-side. I still don't have dual-head set up yet, I'm waiting on my video card. However, I did get the laptop hooked up to the second monitor (which was another small adventure).