[perihelions]

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.

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.

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.