Using alongside Search 404 module

Problem/Motivation

We are currently using the very useful Search 404 → module to redirect 404s to (in our case) a Search API which provided suggestions based on the words found in the user's ill-fated URL request.

This works by extracting words and then then has configuration (shown below) to redirect to the Search API page...

I was wondering if we could combine the two modules in the sense that Fast 404 deals with (and kills off) multiple Drupal bootstrap business that it does so well and then defers to Search 404 to show our suggestions page.

Can anyone help us to understand whether that is a possibility or whether we're barking up the wrong tree?

Thank you