Don't listen to any idiot trying to tell you it hasn't been tried so your Z won't run a 10 second pass. Anyone with half a brain knows that you need 125mph or more to run a 10 second pass in a 5 speed ~3700lbs car. Wheather you will run it or not will depend on the driver and tires. Once you have the trap speeds, its only a matter of time before you run a decent 10 second pass.
I would look into getting a cusco LSD with your setup. You can get it in $800 range.