Talking of complexities, it isn't just the prop that produces drag on an aircraft.
Compared to the free-wheeling prop, the stopped prop will impart more of a twist to the airflow over the fuselage and tail-fin/rudder. After correcting with rudder, you will have more induced drag at the tail. If you end up with any extra yaw, the whole aircraft's profile drag will go up too.
I have no idea how big this effect is!
Edited to add:
A stopped prop probably needs some aileron deflection too.