Hmmm, I did find a way to insert this into the header:
<?php
if (is_null(drupal_get_http_header('X-UA-Compatible'))) {
drupal_add_http_header('X-UA-Compatible', 'IE=edge,chrome=1');
}
?>
And now compatibility mode, even when forced with F12 options, isn't messing up the layout any more! (At least, not that I can tell.) 
So, I GUESS it's fixed now?
Still open to any other ideas and opinions. 