SOLUTION:
I added
$titles = array();
at the top (outside the loop).
Then, within the loop, I used
array_push( $titles, get_the_title( $ID ) );
to collect the titles.
Then I just checked the array for a matching title before displaying, like this:
if ( !in_array(get_the_title( $ID ), $titles ) )
...then do this
And it works!