Instead of trying to do this through the orderby parameter, I went a different direction.
Logically, the orderby parameter above only applies to the posts within each grouping, not the taxonomy term grouping itself so it won’t work for this.
What I ended up doing was adding 01, 02, 03, etc. to the taxonomy term name itself, then stripped that out using PHP. Thus I had terms like:
01 Human Services
02 Education
03 Financial Stability
I numbered these in the order I wanted as they won’t be changing dynamically. Then I used the following to strip out the numbers from the term and echo the updated terms:
<?php
// Output all Taxonomies names with their respective items
$terms = get_terms('issue_area');
foreach( $terms as $term ):
$termed = preg_replace('/\d/', '', $term->name );
?>
<h3 class="expert-term"><?php echo $termed; // Print the term name ?></h3>
Obviously a lot easier than a complex SQL query and gives me the results that I need.
Here is a live example of this: http://pressroom.uw-mc.org/meet-our-experts/
My original question has also been updated with my answer.