Hello David,
Yes, for obvious reasons you could not relay external messages in case you are using a non-authenticated SMTP session (which is the session you have shared).
SMTP-IN:0000BD3C: Set remote delivery to auth
On the other side you mentioned that you have created a rule that is allowing external relaying based on the IP address of your Postfix server (192.168.1.34).
But, from the shared logs we see that the connection came from 192.168.1.36 to Axigen IP address 192.168.1.34
SMTP-IN:0000095A: [192.168.1.34:25] connection accepted from [192.168.1.36:42994]
In case 192.168.1.36 is your own Postfix server and you trust it then please add a relay exception for it like:
WebAdmin > Security & Filtering > Acceptance & Rounting > Routing Basic Settings > Allow / Disallow Relaying > Add IP /Range > Add Exception for: Single IP address | IP: 192.168.1.36 | Allow Delivery: yes > Save
HTH,
Ioan