My dad used to get very angry when talking about the Thetis. He reckoned that Mammoth was in dock and could have easily been used to put a line around the stern and either pull her up or at least drag her to shallower water.
As we all know, the admiralty wouldn't allow anything with very tragic consequences.
Also the MD&HB divers had a Cox's bolt gun that could have fired a hollow bolt through the hull & connected an air line to it, but as you say the Admiralty would not allow any outside assistance.