I figured out how to get My Link Order to use unique id's: around line 191, you'll find the function wp_list_bookmarks. Comment out the line regarding category_before and category_after. Also, change the class to correspond to your css, I made mine 'widget widget_links' since that's the same as the Blogroll widget.
So before:
wp_list_bookmarks(array(
'orderby' => 'order', 'category_orderby' => 'order',
'title_before' => $before_title, 'title_after' => $after_title,
'category_before' => $before_widget', 'category_after' => $after_widget,
'class' => 'linkcat widget','show_images' => $i, 'between' => $b,
'show_description' => $d,'show_rating' => $r,'show_updated' => $u,
'categorize' => $c, 'title_li' => $cat_title));
And after:
wp_list_bookmarks(array(
'orderby' => 'order', 'category_orderby' => 'order',
'title_before' => $before_title, 'title_after' => $after_title,
/*'category_before' => $before_widget', 'category_after' => $after_widget,*/
'class' => 'widget widget_links','show_images' => $i, 'between' => $b,
'show_description' => $d,'show_rating' => $r,'show_updated' => $u,
'categorize' => $c, 'title_li' => $cat_title));