With regard to the other questions you raise, IMHO, Hawking evidences an end justifies the means motive. He cannot entertain the possibility of an external cause and thus tortures the Big Bang with imaginary time to avoid the meaning. He reveals the motive here:
I can't think of a single example in nature of a thing that has a spontaneously self-generated beginning, "out of nothing," as it were. Maybe there are such things; just I haven't seen one yet. Can anyone here point out to me a single instance of such a thing?
WRT Hawking, A-G I agree with your perception that he is beginning with a conclusion, and is marshalling his "evidence" to make sure his preferred conclusion can be reached. It seems quite an odd way to approach scientific questions....
Thanks for your kind words, A-G -- and for this wonderful post!