The umbrella would probably be more of a distraction to the racers, if it's a white umbrella you could try shooting through it and then drape the back bit with black cloth to help stop any light bleeding. It would need to be near perpendicular to the rostrum to stop the drivers being affected by it.
My idea was to try to have the lights facing at least 45 degree's away from the drivers on either side of the course so the drivers couldnt see the light sources just whatever would reflect from the track.
Mixing the two lights could produce blurry images because the rimlight would be much much quicker than the studio stobe although I wouldnt be too sure if the speedlight would have the power for the key light. Although if you arnt using a softbox the power shouldnt be too bad. Some sort of diffusion would be good to cut down the harsh shadows though.
Whatever way you set them up I would mostly aim to try and mix the lighting to give the cars more 3d appearance than the example shot you posted. The rimlight should help that and make the shots much more interesting. I would think of trying a really low angle to catch the cars against the black/dark background with the rim light they should really stand out.
A 5D mk2 at iso6400 with a 200 f1.8 would be usefull (or a 85 f1.2!) although it might be stretching it buying all that gear to shoot a race :P
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