The answer is somewhere inbetween.
Quicktags (and any dynamic content) are rather hard because the uick tags load when the page is called. The page is called NOT when it is displayed but, because of the way AJAX works, before that. Therefore the quicktags JS doesn't execute in the page.
There are ways of working around that though.. however its on the bottom of the list.
Publish to Draft would be easy to do, but rather pointless - you've already published the post! Changing it back to draft probably means you want the added functionality of the edit screen.
However I plan to modularise it so, if someone REALLY wants that, they can have it ;)