but would Germany and/or Japan actually have had sufficient manpower and materiel to occupy successfully such huge swathes of territory?
They would have done what the British had done so successfully, recruited local manpower. There was a fairly large Indian contingent in the Japanese army in Malaya and , given time they would have expanded this. With an easier time in Burma, because the British having severe troubles in the Middle East owing to the increased volume of German soldiers because of the collapse of the USSR, the Japanese would not have to have been so draconian with the civilian population therefore encouraging them to join an Asian Co-operative Army.
America would have stayed out of it. Roosevelt had assisted the UK effectively as a one man band and as another election was coming up the American population almost certainly would have elected a President who presented a 'no interference America First' policy. Their worries about the Japanese threatening the Philippines would have been settled by an arrangement where the USA became responsible for Australasia.
Then somebody would have invented the atom bomb.