6-core CPU is a great choice, especially since you want to stream while playing. The real-time video encoding will eat up CPU, and having more cores than game instances will allow you to do things like configure the video encoding on some cores, while keeping the game on others. That might be pretty helpful!
Sabertooth X79 looks good. GTX 680 is nice, probably what I would go with as well (noting that my multiboxing rig has a GTX 690 in it).
As far as 4GB vs 2GB, this extra RAM is potentially important, but could also be entirely a waste (if you never reach 2GB+ in use). People with 1.5GB were complaining about running out, but I believe 2GB should easily cover 4x Diablo 3.
Reasons 4GB vs 2GB might be important: the higher the resolution and the number of game instances you want to run, you need spare video RAM just to launch the game. This was
much more of a problem back when we were talking about cards with 32, 64, 128 and 256MB. If you run out while playing (after the games are all launched), then you instead get missing textures, which depending on the game means things either start looking the wrong color/texture (WoW used to turn things green I think. EverQuest would turn things white) or will be invisible.
I can't tell you for sure whether or not it's worth it to go with 4GB over 2, but as new games come out they do like to eat more and more VRAM, so you might thank yourself a year and a half from now when you need 50% more VRAM. Or you might kick yourself because a year and a half from now, they come out with 8GB and it's cheaper. The right answer could really go a number of directions.
