Something that is inside-out has the outside part where the inside part usually is. For example, if you wear your tee-shirt inside-out the tag will be on the outside instead of the inside.
The first definition ("To or toward the back or rear") is the closest in meaning to from front to back, which does, I think, have only to do with direction. I would say that from front to back means from one area (front) to another (back).