It's working Rated 5 out of 5 stars
[Edited] Using FF9, with Debian Squeeze. I was trying to move the bar, but I should move the toolbar items placeholder.... Now it's working ok. Thank you Leo!
You don't move the bar itself, you move the "Bookmark Toolbar Items" placeholder that is on the bar, then turn the bar itself off. (That's what I do, anyway.)
As for right-click Customize, the add-on should not affect that at all. You've never been able to right-click Customize certain parts of the Firefox toolbars, with or without this simple add-on. That's just how they work; some things override the menus.