This was my idea--keep the process as it is now; the President selects a nominee for appointment, and the Senate either confirms or denies it. Should the appointment be confirmed, the Judge would serve a minimum of eight years, and in the next election cycle this proposition is placed on the ballot--"Should Judge (insert name here) Retain A Seat On The Supreme Court?" If the voters say "YES" the Judge gets to stay another eight years. If the voters say "NO" the Judge leaves the bench and the nominating process begins again.
This would give the voters more of a say in who sits on the bench, without the polarizing effect of a judicial candidate having to campaign for the office as chief executives and legislators must campaign for theirs. Special interest groups could campaign for or against their retention, of course, but the Judges would at least have a chance to stand on their record, rather than running against an opponent in an election.
Hope that helps.