This is not an optimal answer, but it works well enough for the client to have a page that does what they want. Since I cannot seem to find a function that will do the nested loops as described above, I used a series of query objects, one for each year the client would like to list.
‘$PastConferences2015 = new WP_Query(‘category_name=2015’);
‘while ( $PastConferences2015 -> have_posts() ) : $PastConferences2015->the_post();
This is not an efficient method, in my opinion, because the rest of the code that chooses the fields they want to show is repeated. (I am using the Types plugin to provide the fields they want for the conferences. That is not relative to the question, but it is relative to the efficiency of the solution because each field is called individually and exists in its own layer.)