The simplest solution is to uplift a polite portion of the Earth's mass into an orbital habitation ring, and use a feedback controller to regulate the amounts being launched, to keep the rotational period stabilized (in accordance with conservation of angular momentum) at an integer ratio to the sidereal year.<p>And for the other challenge, to stabilize the variation of the the sidereal year (i.e. the gravities of Jupiter &c. pulling the orbit slightly faster or slower), we simply schedule the launches at either the fore- (morning) or aft- (evening) ends.<p>To anyone sympathetic to my ideology, please consider using "fore", "aft", "port", and "starboard" to refer to the morning, evening, day, and night quadrants of the clock.