Sure ExXB, that is an excellent listing of the problems they face and that many punters will have seen on the various Airport documentary programmes.
I go with the idea that they should have outline contracts in place ready to be activated at a moments notice. That moment would have been as the crew were approaching their time out. For then, it was inevitable that another 2/3/4 hours were in store. That is down to AI. Since they have operated at LHR for a very long time, they know how often flow control is invoked.