Final post on this to summarize:

It now fully works just like the Amazon LightBox Mega Menu

Four files involved

.hvmainheader I added z-index:9999; position: relative;

tpl_mega_menu.php

Code:
I added <div id="mega-wrapper" onmouseover="document.getElementById('fade').style.display='block';" onmouseout="document.getElementById('fade').style.display='none';">
stylesheet_mega_menu.css I added

Code:
.black_overlay{
	display: none;
	position:fixed;
	top: 0%;
	left: 0%;
	width: 100%;
	height: 100%;
	background-color: black;
	z-index:1000;
	-moz-opacity: 0.5;
	opacity:.50;
	filter: alpha(opacity=50);
}
tpl_header.php I added

<div id="fade" class="black_overlay"></div>