Customize: Fix reliability of just-in-time publishing for changesets that miss...

Customize: Fix reliability of just-in-time publishing for changesets that miss their schedule when visiting `customize.php`.

When just doing `wp_publish_post()` for the changeset from `customize.php`, any option-based settings will fail to get saved because `WP_Customize_Manager` would have already been loaded with `settings_previewed`, resulting in `update_option()` calls being short-circuited. So an admin-ajax request to `customize_save` is used to work around this.

Props westonruter, jeremyfelt, dlh for testing, LittleBigThing for testing.
Amends [41626].
See #28721, #39221.
Fixes #42457 for trunk.

Built from https://develop.svn.wordpress.org/trunk@42138


git-svn-id: https://core.svn.wordpress.org/trunk@41969 1a063a9b-81f0-0310-95a4-ce76da25c4cd