would a whip be similar in efficiency to a screwdriver style?
Here's the compiled results of three CA 75m mobile shootouts.http://w5dxp.com/shootout.htm
As you can see, a screwdriver (with top hat) is at the top of the list and a CB whip driven by an SG-230 is at the bottom of the list with a 25 to 1 performance difference. Of course, 80m is worst case for HF but 40m is not far behind. If you give up on 40m and go for 20m-10m operation, the whip/autotuner idea is not a bad choice. But if 40m performance is a necessity, I would go with the screwdriver which does not require a tuner. Usually, a shunt base matching coil is all that is required for low SWR readings.
My 11.5 ft whip with SGC tuner did perform very well on 17m-10m.