For lack of a clean way to do this with DQL, and after a considerable amount of research, I resorted to doing this in Native SQL. Doctrine allows Native SQL via the EntityManager with createNativeQuery().
So in short, I utilized this ability and constructed the SQL query included in my question as a string and then passed it to the createNativeQuery() function.
This does appear to have some drawbacks as it appears I will be unable to use the KnpPaginatorBundle with it... So I might end up just filtering the results in PHP rather than SQL, which I'm hesitant to do as I think there are performance drawbacks.