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Your best bet would probably be a 335 Hoosier autocross tire. Tire rack has them. Although they are technical "treaded", they are very soft and have almost a slick surface.
Y2K is on the right track. Before I went to slicks, I ran McCreary road racing tires that were treaded (with tubes) on my 428SCJ Mach I. Very soft compound tires. I wouldn't recommend slicks for the street. They have very thin sidewalls.
I tried a pair of Goodyear roadrace slicks on a ZR-1 at the drag strip one time, and they were terrible. The sidewalls are so stiff on roadrace slicks that there is no "wrinkle". I put the stock GSC's back on and the traction was much better. The compound/sidewall may be different on the DOT tires? Just my experience. If I were going to drag race I would go with a tire designed specifically for that purpose.
Yes! Nitto 555R Drag radials are available from www.discounttire.com:DThey're only available in size 305x45x18......$225 each+shipping or Call them at 800-739-8999 ask for Brad!
I haven't bought them yet as I understand it's a tall DR at 28.8 inches.I don't know how I'm going to fit it on the car since my car is lowered to 27.25 all around...but I will.The Nitto 555 street tires are really not bad for the track.I have had good luck with them for a street tire.:D