I would like to have add_post_meta to return the ID instead of true or false

According to the Codex, using add_post_meta() you can’t. That function is supposed to return either true or false.

However, that function is a thin wrapper around add_metadata()…

1726  function add_post_meta($post_id, $meta_key, $meta_value, $unique = false) {
1727          // make sure meta is added to the post, not a revision
1728          if ( $the_post = wp_is_post_revision($post_id) )
1729                  $post_id = $the_post;
1730  
1731          return add_metadata('post', $post_id, $meta_key, $meta_value, $unique);
1732  }

https://core.trac.wordpress.org/browser/tags/3.8.1/src/wp-includes/post.php#L1726

… and add_metadata() returns the row insert ID.

Return Values

(boolean|integer)
Returns false on failure. On success, returns the ID of the inserted row. However, note that the return value may instead be the
result of the add_{$meta_type}_metadata filter.

http://codex.wordpress.org/Function_Reference/add_metadata

You can see that in the source as well:

73            $mid = (int) $wpdb->insert_id;
74    
75            wp_cache_delete($object_id, $meta_type . '_meta');
76    
77            do_action( "added_{$meta_type}_meta", $mid, $object_id, $meta_key, $_meta_value );
78    
79            return $mid;
80    }

https://core.trac.wordpress.org/browser/tags/3.8.1/src/wp-includes/meta.php#L31

Given the source to those two functions, I don’t see how add_post_meta() can return a boolean when it is just passing information to, and returning the output of, add_metadata().

I just did a quick test of add_post_meta() on an old (3.6) install on a purely local testing server and I got the ID, not true or false. If you are getting a boolean I suspect it might be “the result of the add_{$meta_type}_metadata filter” as noted in the docs to add_metadata()

The problem could also be related to how your AJAX operates, but you didn’t post any detail, or code, related to that.