At the suggestion of Art Taylor of Old Dominion University, we increased the time steps by factors of 2, 4, and 8. In all cases, the answer converged to the correct AD value. The figure below shows the derivative of coefficient of lift with respect to angle of attack for each of these four timesteps:
The number of iterations 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. We do not know if the CFL number can always be increased, but the technique certainly bears further consideration.