The simple problem is the partisan perception of SCOTUS, but it is a problem well earned by the executive and the legislative branches. They have created this political monstrosity. The solution should be obvious if not easy: Take partisanship off the table. Require, by constitutional amendment, a 2/3 majority of the Senate for confirmation. Broader bi-partisan Senate support will lead to broader bi-partisan public support. Over time, the court may achieve a stable non-partisan balance of 1/3 conservatives, 1/3 liberals, and 1/3 moderates. Something that is absolutely impossible under our current process.