Drag radials do provide somewhat better lateral grip than a standard tire and at 315mm, and provide a fairly large footprint for decent lateral accelleration numbers on the Demon. However, drag radials are not the best handling tires for serious corner burning as they tend to have soft sidewalls that allow a fair amount of deflection, which in a 15" size with a 50-60 series sidewall, will flex quite a bit. For a street oriented tribute car, yes, a 305/60Rx15 square set up of drag radials could give some street going grip, provided you never encounter rain. For general street driving, I think they would be fine. I wouldn't necessarily recommend a drag tire if you were considering autocross events. In this case, a dedicated race tire would be the better solution.

For fair gripping street tires, the selection is limited and in radial construction, none have particularly rigid sidewalls. One of the softest tread and newest carcass designs out there is the Mickey Thompson SR tires. They have a wide range of 15 sizes from skinny front runners to wide steamrollers. Nitto has a series of drag radials, some that have reasonable tread designs that may sacrifice ultimate grip for acceptable adverse weather capability.