Search in custom post types does not find all results

We are using Ajax Search Lite with Advanced Custom Fields and set ASL to search in specific custom post type fields. The search results for autocomplete suggestions find some custom posts, but fail to find all posts that should match. ASL behaves as if it does not search postmeta custom fields at all and only searches in the regular post data.

After researching existing posts, I already tried to deactivate and reactivate the plugin. Nothing changed. I also tried activating the setting Search all custom fields but that yields too many unrelated results. Our custom posts are generated by an import script. We don’t use external Google functionality.

The error occurs consistently on two instances, but it does not occur in a third instance that I have set up on localhost.

These are our ASL settings (without nonces and visual frontend preferences):

wp option get asl_options
array (
  'theme' => 'underline',
  'override_search_form' => '1',
  'override_woo_search_form' => 0,
  'keyword_logic' => 'and',
  'mob_auto_focus_menu_selector' => '#menu-toggle',
  'trigger_on_facet_change' => '1',
  'click_action' => 'results_page',
  'return_action' => 'results_page',
  'click_action_location' => 'same',
  'return_action_location' => 'same',
  'custom_redirect_url' => '?s={phrase}',
  'results_per_page' => '9',
  'triggerontype' => '1',
  'trigger_update_href' => '0',
  'customtypes' => '_decode_WyJjb3Vyc2UiLCJwYWdlIiwicG9zdCJd',
  'searchintitle' => '1',
  'searchincontent' => '1',
  'searchinexcerpt' => '1',
  'search_in_permalinks' => '0',
  'post_password_protected' => '1',
  'search_in_ids' => '0',
  'search_all_cf' => '0',
  'customfields' => 'title|subtitle|description|content|keywords',
  'post_status' => 'publish',
  'override_default_results' => '1',
  'override_method' => 'get',
  'res_live_search' => '0',
  'res_live_selector' => '#main',
  'res_live_trigger_type' => '1',
  'res_live_trigger_facet' => '1',
  'res_live_trigger_click' => '0',
  'res_live_trigger_return' => '0',
  'exactonly' => '0',
  'exact_match_location' => 'anywhere',
  'searchinterms' => '0',
  'charcount' => '0',
  'maxresults' => '10',
  'itemscount' => '4',
...
  'autocomplete' => '0',
  'kw_suggestions' => '0',
  'kw_length' => '60',
  'kw_count' => '10',
  'kw_google_lang' => 'de',
  'shortcode_op' => 'remove',
  'striptagsexclude' => '',
  'runshortcode' => 1,
  'stripshortcode' => 0,
  'pageswithcategories' => 0,
  'primary_titlefield' => '0',
  'primary_titlefield_cf' => '',
  'primary_descriptionfield' => '0',
  'primary_descriptionfield_cf' => '',
  'secondary_titlefield' => -1,
  'secondary_titlefield_cf' => '',
  'secondary_descriptionfield' => -1,
  'secondary_descriptionfield_cf' => '',
  'advtitlefield' => '{titlefield}',
  'advdescriptionfield' => '{descriptionfield}',
  'woo_exclude_outofstock' => '0',
  'exclude_woo_hidden' => '1',
  'exclude_woo_catalog' => '0',
  'excludecategories' => '',
  'excludeposts' => '',
  'wpml_compatibility' => '1',
  'polylang_compatibility' => '1',
  'kw_exceptions' => 'JavaScript, Java, PHP ',
  'kw_exceptions_e' => '',
...
  'classname-excludecategories' => 'wpdreamsCategories',
  'sett_tabid' => '1',
  'selected-customfields' => 
  array (
    0 => 'title',
    1 => 'subtitle',
    2 => 'description',
    3 => 'content',
    4 => 'keywords',
  ),
  'selected-showcustomtypes' => 
  array (
    0 => 
    array (
      0 => 'post',
      1 => 'Search in posts',
    ),
    1 => 
    array (
      0 => 'page',
      1 => 'Search in pages',
    ),
  ),
  'selected-exsearchincategories' => 
  array (
  ),
  'selected-excludecategories' => 
  array (
  ),
  'asl_cf_search_nonce' => 'REMOVED_SECRET_DATA',
  'asl_sett_nonce' => 'REMOVED_SECRET_DATA',
  'wdcfs_15' => '',
  'selected-customtypes' => 
  array (
    0 => 'course',
    1 => 'page',
    2 => 'post',
  ),
)

How to make sure ASL searches in the custom postmeta fields and lists all relevant posts?
Or is there a filter hook to override / replace ASL search logic with our own WP query?