For those encountering the same problem, we have (mostly) resolved our issue by installing the plugin called Relevanssi (https://www.relevanssi.com/), which allows you to replace the default WP search with a powerful search tool and a lot of customization options.
Most importantly, it allows you to continue using the KLEO Ajax search while replacing the awful WP search on the results page with the Relevannsi Search. Highly recommend this.
Brian