As the subject line says
As a network client, EchoLink is not very configurable. It does not have the ability to route to specific NIC’s or gateways. Outbound EchoLink registration will happen from the same interface that AllStar is running on. However, there are work-arounds at the router level.
Are the two NIC’s in use going to separate routers or do you have a singular router serving both LAN segments (AREDN & Public)? If you have a singular router, you can accomplish what you need with some advanced router rules (if you have a capable router). Using source routing rules, you can direct the outbound traffic from the EchoLink module to the public segment by using conditions like the source and destination IP’s (the destination is the EL reg servers).
I do something similar with running two EL nodes on one AllStar server instance. One follows the default outbound route and the second is steered to a second outbound IP. Your solution is similar as you want to steer the EL traffic to a different outbound network.
Just thinking about this a little and it might be possible to steer the outbound at the OS level of the Allstar server using iptables or similar routing rules. I’m not an iptables expert, so can’t really help you there. I prefer to do it at the network level.