I have not tested this but it should be what you are looking for. You can simply use the user field type which returns the user id. This will override the default user id system with your custom one as it makes this change after the post was saved.
function my_acf_save_post( $post_id ) {
// get new value
$user_id = get_field('CUSTOM_AUTHOR');
if($user_id){
wp_update_post( array( 'ID'=>$post_id, 'post_author'=>$user_id) );
}
}
add_action('acf/save_post', 'my_acf_save_post', 20);