Do not go public, keep your anonymity. Going public attracts the wrong sort of people.
Get professional legal and financial advice and enjoy your financial freedom in peace and quiet.
Your rule #1 doesn't apply to most Americans. Only a handful of states allow us to collect winnings anonymously. Meaning, unless we drove hours to and from those states every time we wanted to buy a ticket, claiming anonymously isn't possible. I wish it wasn't so, because like you, I believe many of the issues arise from just the notoriety of being a lottery winner. Except in this particular case. This guy's problem was that he was financially retarded. Had nothing to do with people knowing he won.