Router – Exposing LAN with Zerotier when using Ubiquiti Edge Router X

Well, load balancing and 'failover capability' are two different things. The Windows Server OSes have failover cluster capability, which is what you should use. The following is taken from here:

A failover cluster is a group of independent computers that work together to increase the
availability and scalability of clustered roles (formerly called clustered applications and 
services). The clustered servers (called nodes) are connected by physical cables and by software. 
If one or more of the cluster nodes fail, other nodes begin to provide service (a process known as failover). 
In addition, the clustered roles are proactively monitored to verify that they are working properly. If they are not working, 
they are restarted or moved to another node. 

Update

For custom software, I would recommend using at least two HyperV nodes in a failover cluster. Each one can have a virtual machine tied to the cluster that has your software installed. Without recoding the app, if the primary vm goes down, and can't be reached by the other(s), the other node will take over. See this example.

I've been able to do this by changing the ip address where the gui listens. I'm sure it might be good to additionally set up some firewall rules for this. Here is what worked for me on the CLI.

configure
set service gui listen-address 10.0.0.1
set service ssh listen-address 10.0.0.1
commit
save
exit

By default, the IP address for eth1 is 192.168.1.1, so you may have to change the above to point to the ip address of your LAN's gateway (interface's IP address).