Yep, this is nasty issue that to have full WordPress environment you need to spend considerable time loading it.
I’ve needed much better performance (for very dynamic incremental search feature) for work and what I went with is:
This provides very limited environment, but performance is way way better and reasonable degree of compatibility with WP (starting with
$wpdb) is retained.
Here is start my loader file, not pretty but works for specific needs:
require( ABSPATH . WPINC . '/formatting.php' );
require( ABSPATH . WPINC . '/meta.php' );
require( ABSPATH . WPINC . '/post.php' );
// stuff goes here
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