The Crown could not refuse assent without launching a coup d'etat against parliament in circumstances that would have produced outrage against the Crown sufficient to result in an election that would surely return a ministry bound to dismiss the existing Governor General, and, potentially, force a republic. Westminster inspired Crowns have generally sought to avoid such monstrous controversy, and the exceptions (to my knowledge Lang in NSW, Whitlam in the Commonwealth of Australia) have been intensely divisive.
The King or Queen or the Governor General could not legally refuse assent without having dismissed the executive council (effectively dismissing a government) and thus appointing a new executive council to advise them to refuse assent.
The Governor General could not have legally advised the Monarch, and the Monarch could not have legally advised the Governor General on this course. If the Monarch chose to intervene, they would have had to done so in person.
Such an action would have been an extreme and highly controversial use of reserve powers, amounting to a coup d'etat by the Crown over a policy issue (a bill supported by parliament). Compare to the outrage in Australia when the Governor General had at least the excuse of a blocked supply bill as a fig leaf for what I believe amounted to a coup.
Sources: HV Evatt 1936, The King and His Dominion Governors, 298-300ff
question originally drafted here: Draft of a proposed question