I'd use Solution 1, first of all you get much better quality with DVI than VGA as VGA is analogue (and so I have found with my 1080p monitor, had flickering with VGA).
I'm not attune to the nVIDIA control panel, but sometimes resolutions are locked due to you having a specific refresh rate, try changing this, it's normally 60Hz.
Then, your monitor should have a setting called Overscan, try adjusting this if the desktop doesn't fill the screen (i.e. there's a black box around it).
Hope some of that is some use!