Alignment marks on the motor shaft, coupler, and screw would tattle on a loose coupler. Easier said than done on some machines.
I'm wondering if missed steps from over aggressive machine settings could cause the same effect ? Try replacing the G00's with G01's using your favorite text editor. Think of it as a fishing expedition
I had a similar problem caused by driver timings but that's not a common cause. I'm with microcarve, the simplest answer is usually the correct one.
Anyone who says "It only goes together one way" has no imagination.