The DH problem is due to DNS wildcarding (lack there of) and the fact that websites are not wildcarded.
In DH’s Apache config, it will have a line that says: ServerName www.domain.com
What you need is this line added: ServerAlias *.domain.com
With a wildcard DNS *.domain.com pointing to the same IP as www.domain.com
However, I do not expect DH will add this for you. Unless you know somebody on the inside and a big wad of cash, I’d have to say you’re SOL, unfortunately.