I did try to get a hFOV estimate by moving the car to the start/finish line and setting the car up so I can see the start/finish line in a straight vertical line at the edge of the screen. Doing this I pretty much exactly came to a FOV of 80° (maybe a tiny bit more)
I've just been pondering FoV, as I know I'm too far from my screen, based on my preferred viewing distance when using a controller, which is much closer than I can get when using a wheel.
I replicated your experiment, though I used the white line of a straight section of track instead, as it seemed easier to line up a longer line on the screen. I don't know if this is what you did after doing that, but I used a protractor to measure the angle of the car from the little red marker on the track map relative to the direction of the track, and the field of view is then double that angle. I got a very similar result to you, I got 78 degrees.
I then validated this method by using my camera on a desk to line up the edge of the desk with the edge of the frame, and measured the angle of the camera to the desk. Double this angle matched the focal length of the lens, using an online table of focal length vs field of view, to within a degree or two.
There is an error in the formula posted above, the correct formula is
Distance from screen = Width of screen / ( 2 * tan (fov/2) )
It actually doesn't affect the posted result much, because 1 / (2 x 0.7) is still approximately 0.7.
So, if we assume the screen is 16:9, the width is 0.8716x the diagonal size, giving:
Distance from screen = Diagonal screen size * 0.4358 / tan (fov/2)
Going with my FoV figure of 78 degrees gives:
Distance from screen = Diagonal screen size * 0.538
The implication of this is that there's really only one sensible option for a screen, which is a 43" TV just above the rear of the wheel base, 23" from my eyes.