Just setting term limits is not enough. All of the drama associated with a SCOTUS pick needs to be minimized or eliminated if possible. I would think a rotation into SCOTUS seats would be preferable than direct appointments. In that way, the POTUS can not influence the current makeup of the court and consequently its decisions.

Members of the SCOTUS would rotate into those positions on a random basis from the appellate courts and serve a multi-year (6?) year term. Instead of nominating judges to the SCOTUS, president would nominate candidates to the District courts. Staffing of appellate court positions would come from the District courts.