Go ahead and drive through Death Valley. Enjoy the amazing landscape and views! Just in case of a break down, make sure you have at least a gallon of water in the car. Most rental cars should make the drive just fine. The worst stress on the car is when you climb the grade out of DV -- you could ease off on the speed, and if it shows signs of overheating, turn off the AC.
No problem getting past the construction after hours on Friday, 8/12. You will need to drive back down to pick up the permits... only they MIGHT leave the permits in the overnight kiosk along the road in front of the Visitor Center. You would call the Wilderness Permit office (day before, I think) to arrange that: 760-873-2483.
But you might want to drive back down to pick up stuff in Lone Pine. Check out the Orientation Notes (link on the left) for more info. The Elevation store would have good supplies. I think you can get bear cans both at the Visitor Center and Whitney Portal Store.
The ribs sound good. But I ain't carrying the BBQ.