If you can consistently access and control the containing element you could try a slightly left-field approach using an onmouseover event on the container.
There's a function called setCapture() which you can call during a mouse event to "capture" all mouse events of that kind for the element it's called against, until a mouseup event or releaseCapture() is called. So you could do something like the following:
jQuery(document).ready(function() {
$container = jQuery("#<yourcontainerid>");
$container.on("mouseover", function(e) {
if (e.target.setCapture) e.target.setCapture(true);
});
$container.on("mouseout", function() {
document.releaseCapture();
});
});
The (true) argument is important (I think, without testing) as it prevents any descendent events firing, which is what you want here.
The mouseout function will then release the capture when it leaves the area of the container.
Will this work? can't say for sure, I haven't tested it in your exact case, but in theory it should!
UPDATE: you can use ".container" rather than "#yourcontainerid" in the JQuery if you so wish to enable this for everything of class container.