Comment 27 for bug 15442

"So in gconf-editor go to apps->panel ->general and find the corresponding entry for you in my case toplevel_id_list and reorder the panels in the list in the order you want them to appear in this case the first is at the edge of the screen."

Thank Odin, and thank you. After switching the order of ids in that list, it worked! For the first time in literally years of using Gnome in Ubuntu, I was able to have two panels at the bottom of the screen in the order I specified.