persuading Nazi spies to become double agents was vital to the success of the D-Day landings and deceiving the German army about where Britain planned to attack from.That was easy -- Britain would attack from Greece and Italy, until Stalin humiliated Churchill at one of the wartime "Big Three" conferences and demanded that the US plan for the cross-channel invasion be allowed to go forward. Churchill still got his way after D-Day by making sure that the do-nothing Montgomery had priority of supply.
given the option of either hanging or turning coat, and those who didn’t hang not only relayed harmless real info along with complete fabrications
Yes, this was my understanding as well. When German V-2 rockets were raining down on England, these ‘turned’ spies radioed back to their handlers the location of the impact. When the rockets missed by miles, their message was that the rockets were right on target.