Jim, remember that the Knights of Malta have little to do with Malta -- it is a very rich charitable organization with limited extraterritoriality for one building in Rome.  Not really exile at all for Burke, as we have seen.

No, to do it right, I might suggest to the Pope that he could look to the peripheries and consider how Cardinal Burke might be positively spiritually challenged by a primarily pastoral position. Consider the mission sui iuris of St. Helena, Ascension and Tristan da Cunha.  Ascension can be fairly nice, and if you are going to be exiled, there is no place more appealing to the true traditionalist as St. Helena.  And there is the peace and quiet of Tristan, far away from , well, just about everything.