I just went back for that one today and finished both A and B spec modes with the premium 69 singray. I chose it because it also counts in that classic cars race on the lowest tier (where it murders everybody).
The catch is that the stingray really needs the customizable racing transmission to get its top speed up, but it is fairly inexpensive from the start, and light tuning with weight reduction turns it into a real beast. It's actually pretty light after that first weight reduction, and it handled just fine.
BTW, the prizes for those muscle a and b spec races are more exotic muscle cars (the b-spec is a cobra). So don't worry about missing out on more exotic muscle because you blew money on a lesser one.