Thanks, everyone. The answer is complicated by the use of their paid extension, Featured Pages, which puts a file in "/parts, "class-content-featured_pages.php".
The layerslider div comes out of a plugin, so there is no way to simply move it up.
Actually there is a heap of related <div>'s before it which also come from the plugin:
<div class="container" role="main">
<div id="content" class="span12 article-container">
<article id="page-184" class="post-184 page type-page status-publish hentry row-fluid">
<div class="ls-wp-fullwidth-container" style="height: 500px;">
<div class="ls-wp-fullwidth-helper" style="height: 500px; width: 1310px; left: -70px;">
<div id="layerslider_2" class="ls-wp-container ls-container ls-noskin" style="width: 1310px; height: 500px; margin: 0px auto; visibility: visible;">
So I've tried to put the shortcode [layerslider id="2"] in the file "class-content-featured_pages.php" and place it in the child theme between ?> and <?php above the "container main" div, but it simply prints out the shortcode and does not display the slider. I've tried it in two different places. So apparently shortcodes only work in posts and pages, and I'm back to square one.
Somehow I've got to find a way to place a widget area before the "container marketing" which controls the three featured pages with pics on the Home Page. When I can I'll follow these steps to get shortcodes to work in widgets, http://wordpress.org/support/topic/how-to-make-shortcodes-work-in-a-widget?replies=4 .
All of which makes life difficult for those who know just enough to be dangerous!
Customizr is a nice theme but it's restrictive in the same way that Windows felt restrictive after the control we had on a DOS machine (if anyone else remembers those days).
For those who like it, Google layerslider to see a good demo.