I have three monitors too, although by choice I only play ED on one. I use borderless windowed so I can use the mouse to take focus away from the game temporarily (for example to read the forum in chrome on another screen). If I play full screen at the monitor's native resolution I can still switch focus but the game will minimise to the taskbar.
If I play fullscreen at a non-native resolution the other monitors flicker a bit as the resolution changes then settle down, this may be where your black screens issue comes from.
To play ED across all three monitors ideally they all need to have the same native resolution, and the desktop settings need to be set (in the nvidia control panel if you have an nvidia card) to 'span'. In the nvidia control panel go to display, set up multiple displays, surround spanning options & tick the 'span displays with surround' option.
Once your desktop is set to effectively act as a single really wide monitor, go in-game & select the appropriate resolution in the display settings.
hth.