I have three monitors and a projector connected to my PC. How I have it set up is I have the side monitors extending the display and the projector duplicating the middle display. This fixes having games start on the wrong monitor and with having a mystery display that you can't see. Plus you can switch between the two without having to restart the game.
I'm not sure about refresh rate though, all my displays are at 60Hz. If it's possible what you could try is setting your monitor to 120Hz, that should help with any tearing that would happen... or disable V-Sync.
FYI, As you may have noticed already, you'll have to manually switch the audio in Windows to the correct destination in this setup.