Kb, I "think" your description is what I did for the hookup last night. I didn't use the "extra" white wire coming out of the light. I then hooked up the black and the white wires to the internal rotary switch of the lamp and the house wires coming into the light. It worked! So I'm assuming I hooked it up correctly......no smoke or sparks afterwards!
It was kind of a pain to reach/stretch where it is located, to hold it up, stuff all the wires in, and screw it to the fixture though with only two hands I needed a third.
One thing that appears to be different. The light is beside a radio and the AM signal is totally destroyed when the light is on. This happened with the old one but it wasn't quite as noisy. We just shut that light off if listening to the radio. Another 4ft flourscent that is under the counter right beside the radio doesn't do it just the one I just fixed. Is the noise something that is common with the newer ballasts?