That is not a problem, I think your other ISP is some WIFI or oen which using authentication for using the internet !
I dont' have much idea about that linksys loadbalanced router but you can easily do that .
All you need to do is apply a method of internet sharing linux available among few..
One I have mentioned is this oen -->
http://www.linuxsolved.com/forums/ftopic115.html
Its particularly doing port forwarding.. Just do that and then if allowed in your router, set gateway, DNS accordingly in the router (Gateway must be IP of eth1 or linux box and DNS as per provided by that ISP)