Best I've been able to do is to resize the unmaximized application window to fully cover both monitors.
Position it ine upper left corner of Monitor 1, then drag the bottom right corner to the right and down until you have it in the lower right corner of monitor 2. I've read that a system scritp can be used to resize an application window and such can be performed from FileMaker so you may be able to craft a system script that your database performs as part of a start up script.
You have a Filemaker window open, and you want to slide it across to the second monitor, to see the Excel document behind it, for example? If you grab the whole FM window and slide, it goes ok, yes?
So, if you open a New Window, can you not slide that to the second monitor, and leave the first window on the main monitor, so you can see both FM windows at the same time?
I don't have a two-screen set-up available right now, but I would have bet that I do that often. Famous last words...