Is it possible to build a Firefox extension that displays a floating, persistent iFrame over the page content?

I know it's possible to add iFrames using XUL. For instance, you can add an iFrame to a persistent sidebar. However, I want the iFrame to float over the page content, not cause the content to shrink. So far, my only option is to add the iFrame to the DOM, then use CSS "fixed" positioning to float the iFrame.

The iFrame must also persist across page loads, exactly as the sidebar does. Adding an iFrame to the DOM, unfortunately, causes the iFrame to vanish when the browser renders a new page (e.g., after clicking a link).

Any clues?

Thanks!