Burke was the kid who reminded the teacher when she forgot to assign homework. A bishop once told me that two things occur when a man becomes a bishop: He never has another bad meal. And no one tells him the truth. Burke desperately needs the kind of friend who is not even a little bit impressed by his offices, titles or positions: the kind of friend who will tell him when he's full of sh*t, and won't mince words. I don't know whether he has that sort of friend, but I think he probably doesn't.
In 1968, Paul-Émile Cdl. Léger, who was then only a few years younger than Burke is now, resigned the See of Montreal and, with the permission of Pope Paul VI, went to Cameroon as a missionary. I don't know whether Burke is cut out for something like that, but Leger's example suggests a way forward for Burke. Burke could be appointed as an auxiliary bishop or even an assistant pastor, accepting the authority of a seasoned bishop or pastor. Precedent: Cincinnati once had an auxiliary archbishop.