I realize that what I’m asking is a version of this question:
http://support.advancedcustomfields.com/forums/topic/wp_query-search-results-with-s-and-meta_query-at-the-same-time/
But the solution is to modify the query. I see that I can modify the $args for the query, but not the query itself. Is there a way to modify the query that is performed to do the AJAX search for relational objects?