Mep, your calculation and reasoning in applying Bernoulli's theory
over a car are correct. The static pressure over the top of a moving car is lower
than the ambient static pressure. The downforce on a racing car comes from the static pressure difference between the upper car surface and the lower car surface. As long as the lower car surface can induce a higher air velocity under the car (therefore a lower static pressure than the upper surface) the resulting force due to static air pressure will be downwards, hence the use of diffusers
Mep, also as you said, with increasing air velocity the force you calculated will increase. Your calculation is equivalent to a lift coefficient
Lift = 1/2 * rho * V² * Area * CL
Where CL (Lift Coefficient) = R² - 1 and R is the area ratio you mentioned and took to be 2.
Of course my use of lift coefficient is this case is really a downforce coefficient.
Now Bernoulli's theory is only a starting point for such calculations. I believe Colin Chapman discovered
ground effects performing a similar analysis, so you are in good company. However, to better estimate reality requires acknowledging viscosity effects. Say hello to wind tunnels and CFD…