Combine multiple separate lists into one

You can use a multidimensional array to get this format. Please see the example given below:

$terms = get_terms(
    array(
        'taxonomy' => "issueCompanion", 
        'hide_empty' => false, 
        'fields'=>'all'
    )
)

$multi_arr = array();

foreach($terms as $term){
    $year = get_field('published_year', $term->term_id);
    $multi_arr[$year][] = $term->name;
}

When you print this $multi_arr you will get the format you want. So you can manage your code according to this.