Faking a reverse DNS lookup

So we came across an oddball issue the other day.

Box-a is a mail server in our DMZ with a 10.x.x.x address. The perimeter
firewall does NAT from a public address to and from it.

Ditto for box-b, a public name server.

Now mail needs DNS, so box-a does all of its DNS lookups against box-b.
Unfortunately, it needs to use the public IP address of box-b because the
first thing that a DNS query does is a reverse lookup on the server's IP
address, and box-b does not serve up DNS for our 10.x.x.x space. (In fact,
we don't have a DNS server that addresses 10.x.x.x at all).

Short of standing up a 10.x.x.x DNS server in the DMZ, does anyone know
how we can actually have box-a do DNS lookups directly against the 10.x.x.x
(i.e. "real") address of box-b, thus avoiding the constant passing of
traffic across the firewall?

Thanks,
Colin
.

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