I'm suprised they weren't given the electric chair. I know there were several Nazi spies who were executed using that method, which was typical for that day.
I have been unable to find the rational for this method of execution, as Leavenworth did not execute American's in this manner, as noted in your comment.
Maybe that is what the German's demanded. I mean, they could have built a gallows. I believe about 10 years ago, a prisoner was sentenced to death and he actually worked on his gallow's where he would be hung from .. it was on the east coast side of the country.
Should research this before posting, but I am firm on the memory just forgot the location.
Seems it would be easy to build a stand to hang a person, instead of using an elevator.