First of all, I have never seen your router so I cannot tell you if it can handle it.
Only someone who has the same device can tell you definitely. I would recommend trying to play with these settings on some test network with other routers. That means creating local network with two different ip addresses on your router and trying to send data to those addresses from different devices to see if it sends data to correct servers.
From what I looked up on the internet - the router is not that much manageable on lower levels. If you don't make it work by yourself, I would recommend getting another router that you can surely use to do this (for example mikrotik is in same price range or some used older cisco).
However there is another option which I think may help you and that is reverse proxy- for example nginx. It can route traffic based on ip or hostname in a lot of cases (mail, http and ssl). That would mean the traffic goes all to one server (the reverse proxy) and then the server decides where to send it.
TLDR answer: play around with it, buy managable router or use reverse proxy
Edit: For those settings on the end of your question, it might work if you would fill "Network/Host IP", "Netmask", "Gateway", "Metric" and "Interface" as <Public IP 2>, 32(or 255.255.255.255), <IP of server 2>, [0,1], <interface with cable leading to server 2>