Don't waste your money on headers, they are good enough. They are actually on of the better parts of our cars. If you had a 5-speed, I would think you could beat the kid, but the stock automatic makes it kind of iffy. Go for the pulleys. Don't get a set of sticky tires - they do nothing for a stock automatic because you cannot launch nearly as hard as a 5-speed. If your in need if new tires, maybe look at a set of Nitto's, but I wouldn't go out and look specifically for tires as a mod to get you to beat this guy. Nitrous is a good idea, but you should seriously consider upgrading the fuel system when using nitrous because of the risks involved. You have to run colder plugs, more fuel pressure and way less timing with nitrous. So you would basically have to tune your car to race, then tune it for the street. Kind of a PITA. I say try to find a used GT40 intake on eBay. They go for like ~$300 for the complete upper and lower. After the intake and pulleys, you should see about 240 RWHP and 300 RWTQ. That should be plenty to beat this dude.
Go over to the V6 forums and see what kind of times those guys are running with a supercharger, then we will be able to tell you what you need to do.
Joe