Hi Paul,
I’m afraid the asp_query_args is not going to help here, as you want a union of two result sets – one matching the phrase, and another one not matching but belonging to a certain category.
For this to work properly, you would have to completely edit the core search to add a separate criteria (with a left join query) to include the required items as well.
While it sounds simple, this is actually requires a decent modification, unfortunately I cannot suggest a few lines of code to make this work.