Search Function

I’m finding the search function is not great (i guess this is a WP issue) But I have got great results using the SearchWP plugin. I can weight relevance rather then publish date as the standard search seems to (who needs that?) Anyway all good on a search page but I also love the AJAX search function on the menu bar, however this isn’t updated by the Relevanssi plugin.

Would you have any directions of how I can get the awesome AJAX function to reflect the SearchWP search results? Thanks for any help and this great theme.