We increased the time steps by factors of 2,4, and 8. In all cases, the answer converged to the correct AD value. The number of iterations was reduced by factors of 2, 4, and 4. Apparently, increasing the time step by a factor of 8 does not improve the convergence any more than a does a factor of 4. The figure below shows the derivative of ``coefficient of lift'' to ``angle of attach'' for each of these four timesteps.
We do not know if the CFL number can always be increased, but the technique certainly bears further consideration.