Optimizing a Large Directory Page with numerous Query_posts

I’m working on this page: http://myalumnibar.com/schools/
the goal is to create an alphabetical listing of schools by getting a separate list for each letter of the alphabet.

I want to get all the posts by letter individually so that I can separate them as lists with individual headings and eventually make the entire thing a javascript menu. The current code produces exactly the results I am looking for, but is horribly inefficient and results in incredibly long load times. I’m looking for suggestions to optimize this page somehow so I don’t have to make 26 individual queries.

Currently, this is the function I have setup to run the query for each letter:

<?php function AlphaList($first_char) {
echo "<ul class=\"schools\">";
    global $post;
	//Query posts that are children of the specific 'Schools' category, exclude those in the Trivia category ($SchoolscatID and $triviacatID are globally set in a separate file

	$myposts = query_posts('numberposts=-1&child_of=' . $schoolscatID . '&cat=-' . $triviacatID . '&orderby=title&order=ASC')

		foreach($myposts as $post) :

		//get('School_name') is	the custom field created by Flutter (plugin) that specifies the school's name

		$schooltitle = get('School_name');

//$schoolletter gets the first letter of the School Name from each post

		$schoolletter = substr ($schooltitle, 0, 1);

//If the Schoolletter is the same as the functon paramater, then get the name of the category each post belongs to which is a child of the main 'Schools' category (cat id= 33); If the letters dont match, then dont do anything.

	if ($schoolletter == $first_char) {
	$catlink ="";
		foreach((get_the_category()) as $category) {
		if ($category->category_parent == 33) {
		$catlink .= $category->slug;
		}}

//For these posts, display a link that takes you to the category archive page
		echo
		"<li><a href=\"" . get_bloginfo('url') . "/category/schools/" . $catlink . "\">" .$schooltitle ."	</a>
	</li>";
	}else {
	continue;
	}
	 endforeach; //Done with the posts now
	echo "</ul>";
}

?>

And then every letter is separated like this:

<h3 class="menuheader expandable">A</h3>
<ul class="categoryitems"><?php AlphaList("A"); ?>
</ul>

<h3 class="menuheader expandable">B</h3>
<ul class="categoryitems"><?php AlphaList("B"); ?>
</ul>

<h3 class="menuheader expandable">C</h3>
<ul class="categoryitems"><?php AlphaList("C"); ?>
</ul>

Anyone have a suggestion for how to rewrite this to help speed up the page significantly?

Thanks!