Replacing term/taxonomy archive pages with search queries

I’ve got a site with a very large number of custom taxonomies. The site uses FacetWP to allow uses to drill down through those taxonomies. Instead of sending users to taxonomy-{taxonomy}.php when they click a linked term/taxonomy, I’d like to send them to the search with that specific facet applied. FacetWP makes this very easy with query strings.

It seems silly to use wp_redirect() and have 301 redirects for hundreds and hundreds of items. Is there an easier way to programmatically replace what WordPress considers the destination for term and taxonomy archives?