30-35 MPH at half throttle doesn's sound right and could be a clue.. some kinda carb or cable adjustment problem or something.
Or maybe an RPM related problem..maybe the points start floating at some high RPM, due to a weak spring? Maybe something else in the ignition/magneto is loose or somehow causing troubles when it spins real fast.
Of course the carb could be part of it too. Half throttle is right in the middle of critical needle range.. maybe drop or raise the needle a notch and see if there's a difference.