I want to move the 'change desktop' icon to the bottom of he unity bar, next to the trash (I'd actually like to get rid of the trash, too...), but I can't find any options for that anywhere. How would I do this?
I am running Ubuntu 13.04 (Raring Ringtail) 64-bit.
Currently you can't remove the trash icon from the launcher. Here is the rationale behind that. So I don't think you can move any other icon to the bottom also.
Have you tried Gnome? http://www.gnome.org/gnome-3/ You could update from what you currently have: go to Ubuntu Software Center (or Synaptic, if that's what you use) find Gnome Shell, and install. You'll have to choose Gnome after your next reboot. Notice that moving the mouse towards the upper left makes the program bar appear. You can drag icons to this bar in any order you want, or delete from too, if that's your desire.
Or, you could install http://ubuntugnome.org/ 13.04
