I'd suggest elevating more federal court justices for a period, durich which time they decide as a group what to take up and then randomly assign 5 or 7 to a case. After their stint they can either return to federal court or retire.
If we're comparing with the current SC everything is an improvement. But if we're going to change things, I would prefer a system that does not rely on easily manipulated, uneducated masses.
I haven't heard of a lot of jury tampering trials go well. And usually isnt it more of a mafia style "nice family you got there, would be a shame if something happened to it" situation?