Try adding edit_date => true
to your bmt_post
array, like so:
$bmt_post = array(
'ID' => $post_id,
'post_title' => wp_strip_all_tags( $title ),
'post_content' => $information,
'post_status' => $post_status,
'post_category' => array( $cat_ids ),
'post_date' => $post_date,
'edit_date' => true
);
If you look at the function wp_update_post
found here: scheduling posts with wp_update_post you can see that scheduling won’t work without this parameter being set
Hopefully this solves your issue?