If you want to show only the living hinges bent, you should be able to do it by making the spine 2 parallel straight lines, separated by maybe .001" (it won't let them be colinear), with a small loop right where the hinge actually is. Use an evaluate feature to make sure the length of the spine, the location of the loop, and the straight lengths are correct by driving the sketch of the spine as a perimeter dimension. Make sure you select the "constant length" (if I remember) option, AND specify the length to bend like you had to in previous options to prevent distortion. Not at work so I can't verify, but that should work. Then you can make a family table instance of it.