Regarding: "But the meta-question is, should the Catholic Church still believe that doctrine must be logically coherent? "
- This is a very good question.
- Doctrine or magisterial statements can be set aside when the facts of the matter show that either the doctrine is misconstrued, or that it has been so poorly stated as to be unhelpful.
- However as to the concerns of the 4cards and their hidden supporters the real issue is not 'if this, then not that', or 'there can be no 'ands' connecting magisterial statements and or doctrine', but that doctrine and magisterial statements are connected and found worthy in pastoral practice.  
- If the church has discerned that pastoral necessity requires a new 'lens' to see, then it is for the church to determine what lens that might be. That lens might not be everyone's cuppa but if the bishops with the Archbishop of Rome says it has merit, then we can only work for its success, until in practice it does not work anymore.