The solution is crystal clear, though: impeachment.
If Thomas really is as bad as so many of these stories say, then Congress should apply the solution they have in their hands and impeach the guy, removing him from Court.
OR, if he's not actually found to be as bad as all of these stories, if the stories are a bit out there, then it's not really a problem to solve.
Either way, impeachment is on the table, and that will work itself out.