I figured this out by putting the main menu slug into the show_in_menu key of the custom post type array like so:
$args = array (
'labels' => $labels,
'hierarchical' => FALSE,
'description' => $title . 's',
'supports' => array( 'title' ),
'show_ui' => TRUE,
'show_in_menu' => 'squirrels_inventory',
'show_in_nav_menus' => TRUE,
'publicly_queryable' => TRUE,
'exclude_from_search' => FALSE,
'has_archive' => TRUE
);