Swales in ancient fields

I'm going to be building swales in our field with a rotary plow, I guess in a month or two depending on weather. Our fields are land that was in my wifes family as well as some adjoining fields we bought. I have a surveying level, so finding contours isn't a problem, except for one thing. Fields here were originally long and narrow, and in the case of our fields where I want to make the swales, the long direction is pretty much going from up at the top of the ridge to down. The way they were plowed, over centuries I guess, means that each narrow field-strip is higher in the center and lower at the edges, with a difference of 1-2+ feet (more on strips that have trees and thus didn't get plowed much by tractors). So this means my field has the equivalent of 8 or so ditches running downhill.

How do I account for this with swales? Do I just dig down deeper in the center of the field-strips until the bottom of the swale is level?

I'm attaching a sort of map showing our overall property. The brown-dashed lines around the perimeter are property lines, and the dotted brown lines inside show these field-boundaries. The yellow line is approximately the top of the ridge, to the right of it is gently sloping downward, but is fairly flat to the road. The slashed area is about 1/2 acre that I will be planting corn, potatoes, pumpkins and other things that won't need much attention, but hopefully will benefit from the extra sun at the top of the ridge vs down in the bottom of the valley near our house.

Some photos of the field. These rises and ditches are best visible in the photo with the power lines, as that shows some of these field-strips that weren't plowed because they have/had cherry trees, but was cleared under the power lines. Google Photo Album

Swales don't have to be dead straight. You could zigzag them gently to keep on the contours. That would require less digging and minimize steep slopes above and below the swales.