Demonstrating how I fit the back to the sides. When describing the different radii involved I occasionally refer to one as the other, and I make a few other faux pas, so to be clear I'll explain:
1. The radius that the back braces are shaped to is smaller than the radius of the curvature from the bottom on the body to the neck. In fact the longer curve is most definitely not a radius at all, not a part of a true circle, but if it were it would be most definitely a larger one than that of the back braces. If I used the same radius all around the back would have much more arch along the grain.
2. If I glued in the linings prior to rough shaping the edge of the sides, and then shaped the sides, the linings would get narrower everywhere but the waist, and not the other way around.
3. I occasionally refer to the back as the top, but you've figured that out already.
4. Toward the end I say that if when pressing the ends of the back down so that the brace ends touch the body, it takes a lot of pressure to do so, that the brace is too high. I meant to say that in this scenario the waist is too high.

The guitar will be a Port Orford cedar classical, with a Port Orford neck and red cedar top. Some of the best classical guitars I have built have been with cypress (POC) back and sides. They aren't as loud as rosewood, but the color of the sound is exceptional.

For more information about my guitars and lutherie instruction see my website:
http://www.obergguitars.com