Run them all on a 45 degree angle. The pieces will all be shorter and it always looks classy!
-----------------
That's ignoring wood movement. Doing it that way you're guaranteed to get more and larger gaps between boards as the wood moves with the season.
I'm also not sure that cutting every board and running the boards across the width of the hallway would work for other reasons. When you buy wood strip flooring the bundles are of assorted lengths. They're not all 40"+ long. You could specify that when you order them (or make them), but you'd be paying out the nose (or sucking down way more time then any potential time savings in laying them AND paying out the nose).
If someone is going to go to all of that effort, they certainly should dress up the hallway with feature strips, etc. Not sure if that's what the OP has in mind for his time and money.
R