The founder of AA, Bill Wilson, was handed a copy of William James' "The Varities of Religious Expereinces" by his friend, Ebby Thatcher, who was a member of the Oxford Group, for which the book was recommended reading material. Ebby told Bill that his own alcohol problem was solved when he found God, in the Oxford Group, led by Frank Buchman.
Bill Wilson joined the Oxford Group, after his spiritual 'white light' experience whilst undergoing the 'Belladonna treatment' for alcohol detox at Towns Hospital; whilst visited by Ebby and other Oxford Group members, as part of their religious conversion program.
Bill W. credits William James and his book, in the AA Big Book, Chapter Two, "There is a Solution": "The distinguished American psychologist, William James, in his book “Varieties of Religious Experience,’’ indicates a multitude of ways in which men have discovered God. We have no desire to convince anyone that there is only one way by which faith can be acquired".
I think it's fascinating that part of William James' 1902 book which the OP set out, explains the divided self known as "ambivalent" in AVRT:
"Along with the wrong part there is thus a better part of him, even though it may be but a most helpless germ. With which part he should identify his real being is by no means obvious at this stage; but when stage 2 (the stage of solution or salvation) arrives, the man identifies his real being with the germinal higher part of himself; and does so in the following way. He becomes conscious that this higher part is conterminous and continuous with a MORE of the same quality [authentic self] ... which he can ... in a fashion get on board of and save himself when all his lower being has gone to pieces in the wreck."
Since James' book a century ago, science has proven the lower and higher brains (lower autonomous, habits, compulsions etc.) higher brain (seat of logic, can weigh up repercussions and override the lower brains urges). Buddhism and many religions realised this centuries ago.
So as William James said, man can save himself, Authentic Self trounces Lower Self, therefore no requirement for God's input. As a spiritual person, one could say that God is the creator of the Authentic Self, that still, small voice inside, that knows right from wrong, that can stand apart and override the clamouring ranting of the automatic, habitual, lower brain Beast shouting for ITs alcohol fix.