Setting Up Public DNS (Split-Brain?)

We host our own website on our DMZ, which is a non-routable segment attached to a F/W (all DMZ hosts are NATTED with routable public IP addresses).

Our current situation is we have one internal DNS server resolving both internal and external requests. We allow a hole in the F/W for external DNS requests. We want to change this so any external DNS requests ie. to our web server are resolved by another DNS server on our DMZ.

I read the (commonly quoted) article at URL which basically advises that I set up the new (Primary) DNS on the DMZ with the same zone name with just the publicly accessible hosts ie. WWW, which I have done. Furthermore I am advised to configure the internal DNS as a Forwarder and Slave to this new DNS in the DMZ (for unresolvable and recrsive queries). Fine so far..

I set up a basic test - set up a new DNS on the DMZ, configure the NAT so it can be routed to/from, enter the zone (same zone as the zone on our inetrnal DNS) and add the relevant hosts. So this new DNS is authoritative for the zone mycompany.com and I have a host for our website URL.

nslookup from the new DNS to the WWW record is fine. However when I go to an external PC enter nslookup and change the server to the public IP address of the newly created DNS on the DMZ and then do a query for the www record I just get the error "DNS request timed out...Request to DNS server timed-out". Our F/W shows nothing amiss.

I would very much appreciate some advice on how I might get this external DNS working.