LONGBOX from what I've read the reason the ZR1 was not a success was because the Supercar buyers didn't want to own a Chevrolet. Won't this new Corvette have the same problem?
REBEL, its not so much that I don't think it can be done, its that I know it can't be done easily. You've narrowed the target quite a bit by saying you want to win a stop light to stop light race.
I know you don't actually expect to encounter a Z06, but let's use it as an example of your competition anyway. This car weights just over 3000 pounds, has near perfect weight distribution and computerized traction control.
Those guys have trouble getting the tires to spin, not because it doesn't have enough power, 505 horse is plenty for that, its because the computer controls application of power to the tires to keep from wasting any spinning tires.
You are driving a short box pickup (I think you'd do better with a long box) with a heavy front weight bias. Go with a 454 and 4.88 gears and you'll easily spin your tires stop light to stop light.
Coilover has a good suggestion, put the motor in the bed. Maybe run that 454 with a Toronado/El Dorado front drive setup, and then you'll have a head start on the traction problem.
Drag racing a pickup you've given yourself a huge handicap. Making it competitive, even just light to light, against an 11 second car is not going to be easy. If my skepticism motivates you, great! Go for it!
But as I said, please post pictures and tell us what you are doing.
I own both a 454 powered pickup and a small block Corvette. If we're racing on pavement I'll choose the 'vette every time. Pulling a trailer I always choose the pickup.