Short answer: You can’t. Getting W3 Total Cache to talk to a non-WP call in manor listed above isn’t (easily) possible. I completely agree with @allenericr comments. The Transients API is very straight forward and quite simple to implement. In addition, @allenericr, comment on using admin-ajax.php is also spot on. It’s not sure it’s best practices to just include wp-load and call it good (sounds like a big security hole).
