<Could it be that Hawking, very much a man of this world and a brilliant one, but forced into an ascetic cell by his illness, has the unique situation and tools to puzzle out the big questions?

Could be. I know that Buckminster Fuller partially credited his terrible eyesight as a child with giving him insight into the larger ideas of form he used later in his life.

As for mystic experiences, there are those (present company obviously excepted) in both physics and metaphysics who sometimes let their concepts of reality rely too much on such speculations, and they start talking about what the heck is real anyway? A rock on top of the head (not too big) can cure this quickly, but the treatment is controversial.