+1 Also check if the transmission has been replaced as the 03/04 models had weaker tranmissions than the later models. Not sure if you can check maintenance history by VIN via the dealer but the part number for the new transmission is: CD009 I believe (which is a much stronger unit than the original).

You should be able to run slicks with the stock diff and all just fine. There are overheating issues with the stock Diff during prolonged periods of extreme use i.e. road racing... don't believe you should be having those same issues on 1/4 mile strip though. Although i wouldn't recommend turning it into a single purpose car (drag queen) as they are meant for much more than just driving down a strip in a straight line.