What? You want American race car drivers to turn right? Close the streets like Monaco, or the Isle of Man TT course, or like the Targa Florio, Mille Miglia, or the Mexican Carrera Panamerican? Riverside and Sebring were popular enough but the Brickyard and Daytona were bigger. In my personal memory, Phil Hill was the first American that turned right. And he had to go to Europe to do it. The American mainstream automobile industry didn't feature good road cars until, let me think. Fairly late. Even Corvettes and T-birds were only made to look like, but not really be, sports cars.
Road Racing had already grown in amateur levels by the 1960s, which saw guys like Carroll Shelby become famous in their efforts, and saw the Shelby Cobra, Mustang GT350, Corvette Grand Sport and others become highly successful in American racing, as well as European racing. Americans participated in F1 as teams into the 1980s through Shadow and Penske, and tried again with Haas Lola in 1984-86. Daytona didn't exist until 1961 (it wasn't built yet), while the Indy 500 was the biggest stage in American racing until the 1990s.
Harmonizing American with European racing is impossible until after WWII, but after that, it's easy. Cars like the Allard J2 could easily battle with the Europeans - hell, a nearly stock Cadillac Coupe de Ville competed in the 1950 24 Hours of Le Mans, and finished tenth, while a rebodied car with the same engine finished 11th. Just get more promoters like Cameron Argetsinger in the post WWII era, creating a number of road racing circuits, thus forming a real demand in America for road racing.
Hell, one BIG WI could be Big Bill France keeping racing on open roads as a major portion of NASCAR, which eventually saw NASCAR evolve into a road racing series.

One other option could be to have Trans-Am continue to be successful, with the rules changes that turned the cars into tube-framed racers in the mid 1970s never happen, with the 1970s keeping the Camaro/Mustang/Firebird racers, with newer import sports coupes and sedans (Datsun 240Z, Toyota Supra, Jaguar XJS, Porsche 928, BMW 635CSi, Rover SD1, Mazda RX-7) joining in the 1970s. In the early 1980s, this evolves into the modern Group A formula, which is modified to allow the bigger engines of the American GTs. The Trans-Am series come back quickly in the 1980s, with the American competitors slugging it out with Toyota, BMW, Jaguar and others later on. The relatively cheap costs of Group A Camaros, Firebirds and Mustangs sees their numbers flood most of the series in the 1980s, and with the advent of the ultimate Group A cars (Ford Sierra RS Cosworth, Nissan Skyline GT-R, BMW M3), the big-banger Detroit iron is developed into real competitors, making big-inch power the way of beating the big-boost Sierra, four-wheel-drive Skyline GT-R and the featherweight M3. The Trans-Am grows into one of America's biggest race series by the 1990s, and leading to a whole crop of racing nuts who want to race in what by then is the world's largest touring car series, and the savior of the Group A formula on paved tracks.