After spending a little while changing just the view script I realized I really needed to change the layout file for my public home page. It turns out this is a little more complicated than changing the view file but not my much.

The first step is to change the layout file in your action. This is done using the $this->layout() function:

$this->layout('layout/public');

Next, in the view_manager\template_map key in your module.config.php file of your module add this line:

'layout/public' => __DIR__ . '/../view/layout/public.phtml',

Finally, make the new layout file and it should work.