I have the exact same video card as you and I have successfully flashed the Bios from an F2 to an F3 the day the new bios came out. I was stumped for a few minutes trying to figure out what software to use. On the day that the F3 bios came out the OC Guru II didn't even show anything newer than the F2 bios so I wasn't able to use that.
I found this link on Gigabyte's website;
http://www.gigabyte.us/WebPage/40/index.htmAnd I used VGA@bios utility. Since you already tried that program and it didn't work for you then I'm not sure.
Have you tried to restart your computer after installing that vga@bios utility?
Have you tried to use nvflash?
A couple of years ago when I was messing around with the GTX 680 bios I wrote down these instructions for myself so I would not forget them. All you would have to do is rename the file from sc680.rom to g780ti.rom for example. This is using nvflash.
"First rename the file to sc680.rom
Now boot to your flash drive with the sc680.rom bios.
this command will flash your card with the GTX 680 SC bios.
nvflash -4 -5 -6 sc680.rom
Press y to all the questions and you're done. If you get an error saying it can't fine the card you may have to specify the port as follows.
nvflash --index=1 -4 -5 -6 sc680.rom"
Make sure to eject the usb flash drive before you restart windows but keep the drive in your computer otherwise you may have read/write errors.
