Ah, but your monitor is still emitting light, even if you set it all to black on a black background. Now if we can get everyone to dig out 8" monitors from the 70s then we'll see some savings :P
....err, I'm not sure my 5" monitor ever drew less than 2.2A, unless it was unplugged!
That doesn't seem likely to be much help.
Of course, the screen was black when it was turned off (well, dirty gray, anyway), so maybe that would fit into the solution: find a way to render the screens on a monitor that's unplugged.