Draw names out of a group of eligible lawyers,judges
This was basically how it was in the Articles of Confederation
at the time of the revolution there were disputes between states over western territories. The states were very interested in coming up with a fair way to resolve the disputes. What they came up with in the Articles of Confederation was a kind of random system where the last step was drawing names out of a pool for the judges.
also have extra names drawn as replacements when main Judges should recuse themselves (which they should probably do more often)
Dream on--LOL. This is a LIFETIME job--no one can fire them--nor will they recuse themselves.
While the court is considered conservative--as we have seen--often unexpectedly--they will approve of something or disapprove of something regardless of party politics.
And that's the way it should be.