This seems tantalizing close to the solution to the problem I’ve had 3 developers chasing for weeks.
Though not a coder …
I have added the above code (unmodified) to my functions.php file. However, when I use the shortcode supplied by John with the two parameters you suggested, the portfolio displays, but the terms do not appear above the items (as they do on the sortable portfolio pages), so consequently I am not able to actually sort them.
What am I doing wrong?