First of all, unrelated advice, update to 7.2.2 to be as much as possible bugs free.

If I understand correctly you are trying to control via GUI server in DMZ from outside. This is not something many admins will like as from what I have seen preferred approach is to connect via ssh tunnel to bck server and from there use cmd to control the server.

7.3 doesn't use connection ports, but 7.2.x still does so you will probably need to pay attention to that too. Also, I believe initial 7.2 release used 111 so... I would start by configuring a slightly wider port range (both service and connection port) and try to do basic operations. If that would fail (or connect itself) I would inspect firewall logs first - the should be good pointer to what is wrong.

Note that you will also need to fix hosts table too - to achieve what you want you will need to add your workstation as client resource in server and that one will need to be recognized by DNS/hosts. Usually inside DMZ there is no DNS at all so you will need to take care via hosts.

From my understanding of what you are saying here, the servers (including backup server) are all within the DMZ, so for backups it does not matter about ports being locked down as you are not backing up across the firewall.

However to be able to run an nsradmin session on a machine outside the DMZ with a Networker client on it my guess is you would be okay with ports 7937 and 7938 open. Do you have any indication of the errors you are seeing when you try to connect?