The constitution isn't the only entity that could fix the size of the court. The court's size was fixed at nine by the Judiciary Act of 1869.

The revisions I proposed could be implemented by an act of Congress.

I would also establish a line of succession, where, if the president and the Senate cannot agree on a candidate, the justice is the highest ranking federal judge who has been confirmed by the Senate since this plan was enacted. Appointment to a federal bench contemplates the possibility that the judge could be elevated to SCOTUS. Confirmation after this point would signify the Senate's consent to this possibility. (I'd make it the highest ranking federal court judge, regardless of when they were confirmed, but that would probably be deemed unconstitutional)