Walk Designer uses the Body x- and z-trans channels to move a figure along the spline path. For some reason, that keyframe data is lost when you export the BVH. Body channels aren't saved in pose files, either. What we need is some manner of Python script that can add the Body x- and z-trans values to the existing Hip x- and z-trans values, then zero the Body x- and z-trans channels. I'd try writing one myself, but I don't know enough Python yet to manage it.