Actually it does seem to be immovable -- I've tried a number of techniques (floats, CSS-positioning, CSS-transforms) and haven't been able to just simply move the control one pixel, let alone to somewhere less intrusive within the toolbox element.
Hiding it without disabling I can do. Here's how:
In your ...Application Data\Mozilla\Firefox\Profiles\..profile..\chrome folder, add the following UserChrome.css
Restart Firefox, and the waste of vertical space is gone.
You can tell how well crafted the control is, when you look at the XUL and see that it's a
toolbaritem naked in the
toolbox, rather than actually being in a