Another thing that could screw up the balance procedure with wall or parachute is if the elevator halves aren't in perfect sync with exact end-points. If this is off, even a bit, it could make things hard to figure out.
True, to a point. As long as you leave them endpoints alone you can still tune the plane to be "inherently stable" or in this case "inherently centered" by using the parachute method. As soon as you adjust the endpoints you have to readjust the lateral CG again. Like I said before, planes like to tell you where their weak points are in the air, not on the ground. Any static tests you do to an airplane will only bring you halfway there, or less.