"Now please correct me if I'm wrong, but I'm certain that neutral ships under escort by warships of one belligerent are fair game for other belligerents. "
Consider this your correction.
You are wrong and that kind of attitude in the war would have quickly cost a U-Boat captain his command and quite possibly his life. Hitler was not out to engage the whole world in a war...not at once any way. He went to great pains in the early days to try and keep Britain out of the war for instance.
One of the great mysteries of the war is why he choose to declare war on the US after Pearl Harbor after spending two years trying to keep us out of it by giving us no excuses to declare against him despite the fact that the US was helping both the UK and Russia with materiel. The terms of the Tripartite pact only required Germany to declare war on any aggressor of its members and Japan was the aggressor, not the US.