Windower can launch as many instances of FFXI as your computer can handle as far as I know. Unfortunately windower doesnt give you an option for which monitor a borderless window is displayed in so for your second monitor you will have to have that instance of FFXI launched in a regular window then drag it over to your second monitor and maximize it. Someone might know otherwise about borderless windows on multiple displays however. If so, please do tell.
The only way I know to do this is to use the command window_toggleframe
This puts a window around your instance which lets you move it around. When you toggle again it takes it away and lets you lock the window in to that new position. You can technically do this in "full Screen" on each monitor. When I first started dual boxing I did this. It's a huge pain in the *** to set up perfectly but I was able to get 2 1920 X 1080 instances with one on each screen. Adjusting the second one is hard since toggle frame moves the frame slightly so getting it exactly on the second monitor took some work.
But the most important thing is that for me, it was disorienting as hell. It was hard to tell which instance had control and I'd end up on the wrong one so often and my brain just couldn't handle seeing both in full screen. I can't tell you how long I tried to get use to it but it made my head swim when I entered a command and only one of the instances responded to it and I guess my brain thought both should. I just couldn't do it.
Eventually I reverted to having both instances on the same side, full screen so i could only see one at a time and that's how I still play now. I can't stand little windows even for my alt so this worked best for me.
But yeah I ended up doing the same as you, both chars on one screen and info, chats browser on the other.