Omega override simple-layout.tpl.php for content types
So, I was able to accomplish this using the following:

tl;dr: Create another layout extension, and use theme_omega_layout_alter(&amp;$layout) to switch.  That's the preprocess function I had to track down.

(assuming use of included layout *simple-layout* and you want to create a layout for node type plain-page [the naming convention doesn't matter])


Copy themes/_your-theme_/layouts/simple to themes/_your-theme_/layouts/plain.  
Modify the file names:

simple.layout.inc -> plain.layout.inc
simple-layout.tpl.php -> plain-layout.tpl.php

Modify plain.layout.inc (It's just like a .info file for a theme, self-explanatory)
Modify plain-layout.tpl.php to suit your needs (In my case, I need to remove everything except render($page['content']).
Open themes/_your-theme_/template.php and add theme_omega_layout_alter(&amp;$layout):

// this is specific to my use case
// change 'theme' to your theme name, as you would with any
// preprocess function
function theme_omega_layout_alter(&amp;$layout) {
  $cPath = current_path();
  if (strpos($cPath, 'invite-print') !== 0) {
    $layout = 'plain';
  }
}



The following is only necessary if you want to change parent structure (&lt;html&gt;, &lt;head&gt;, etc.), which I needed to


Open themes/_your-theme_/preprocess/html.preprocess.inc and put this in:

 // this is specific to my use case
 // change 'theme' to your theme name, as you would with any
 // preprocess function
 function theme_preprocess_html(&amp;$variables) {
   $cPath = current_path();
   if (strpos($cPath, 'invite-print') !== 0) {
     $variables['theme_hook_suggestions'][] = 'html__plain_page';
   }
 }

Create /themes/_your-theme_/templates/html--plain-page.tpl.php and modify as necessary.


It felt like overkill for my situation (having to create entire new layouts) but I understand why it was done - it's crazy powerful for sites that need to make drastically different layouts for different pages.  Think different regions, stylesheets, js, etc - completely different .info files, essentially.

Hope this helps someone!