If we've learned anything over the last few decades......it's that Self Regulation is a pipe dream, a myth, and SCOTUS isn't somehow immune to that just because they're the 'highest court in the land'.
I think they should welcome ethics requirements, as written by congress, that apply to all other federal judicial positions. They should agree that they're not special than any other federal judge, and just deal with it. And if they don't....well then, they'll just have to abide by whatever rules our (broken) congress makes. Whether that means term limits or age limits or stacking the court.
These judges need to stop acting like they're above the law, while they interpret the law. If they care about the Constitution, and expect We The People to respect their decisions, they should act accordingly.
(But I'm not optimistic, since they've ruled that Money is Speech, and Corporations are People. Leonard Leo and the Federalist Society are still freeeee to buy judges, and write it off their taxes.)