Manipulating plugin's code is not the best solution from my point of view.
@Dom's approach seems great but doesn't support the "s" value for gravity's attribute of tipsy, which shows the tooltip in the center of the element tipsy was binded.
My first thought was to detect mouse enter for the container "div" and bind tipsy to the inner header (h2). That won't work for small headers since h2 by default is displayed as a block and takes 100% of the container element.
You have to add some CSS styling to the header which will break up your content.
So I have managed to build up a solution where I wrap h2 contents with a span element in order to keep things clean and clear.
Manipulating your original HTML
<div id="everything" original-title="The whole kit and caboodle.">
<h2>Working with really great and awesome headlines</h2>
....
</div>
to
<div id="everything" original-title="The whole kit and caboodle.">
<h2><span original-title="The whole kit and caboodle.">Working with really great and awesome headlines</span></h2>
</div>
Least but not last, I have polished my code in order to bind tipsy only once for each div container, since I wasn't able to find out how the plugin manipulates the DOM
Updated version as @585connor suggested
http://jsfiddle.net/JqFwP/22/
Update vol2:
There is a another issue with my approach, if the headline is too short, the tooltip is stripped outside of the DOM.
I have managed to solve this using a class in the wrapping span and some css code.
Proof of this issue
http://jsfiddle.net/JqFwP/25/
My workaround
http://jsfiddle.net/JqFwP/24/