Why not using the real IP in the script?
(It depends on the language and what you are doing in the script, though.)
Also, if you simply want to resolve with other DNS, you can use dig or other tools.
dig @dns1.whatever.com example.com
If you want to get HTTP access to your primary, you can use netcat (nc) or Perl/Python/whatever to connect to the real IP and provide domain name for Host: header.
So, the DNS of DH shouldn’t be a big problem, even if it tries to do more than you wanted.
And you can add A record, as you might be thinking to do, too.
Maybe DH can disable DNS for you. Have you asked?
...* I’d be happier if DH had free shared SSL and redundant server setup. ..*.