armature keyframe bake action problem

bakeaction.blend (715 KB)
when you open the blend file, click on pose --> animation – > bake action , and bake it with ‘clear constraints’ and ‘visual keying’ checked

here I have a mesh with an armature, the armature has an IK spline bone constraint targeting a short bezier curve, this bezier curve has a move animation as well as a curve modifier which targets the long curve… the intended effect is that my mesh snakes along the path defined by the long curve

since IK spline and the curve modifier dont work in BGE, I am forced to bake the armature into keyframes… however, once the animation has been baked, it deviates from the original animation, and I absolutely need it to follow the original animation precisely
how do I solve this problem?