Russ,
Corvairs were not initially accepted into SCCA races because they sold as "sporting sedans." . Don Yenko wanted to race them under this dealership's banner so he removed the rear seat, hopped up the engine, tightened the suspension and created 100 of them for homologation. The SCCA agreed that the Yenko Stinger was a separate car from the Corvair and placed them in Class D. They handled quite well but their weight remained high relative to the engine's power. The Corvair 164 cu in [2.7 liter] engine's design meant low rpm and no further room for boring out, so they would lose out to better power/weight ratio cars. As you could see in the video, they were big to maneuver around a racetrack.
With the early models [1960 - 1964], John Fitch created his Fitch Spider, which improved the handling, steering and shifting of those swing axle models. It was not entered into SCCA races at that time, but they're fine handling sports sedans.
Corvairs were entered into the early stock sedan races but quickly beaten by the more powerful Valiants and Falcons. They also blew rear tires and flipped fan belts under racing loads. They were far more successful in endurance rallies.
Jeff