If it is the shutter, it is because it is not running at the same slot width as it traverses the film gate.
The M7 is a spring-driven shutter run, and the electronics just time when to release the second curtain. After the shutter curtains are released, it is up to the smoothness and spring tension to make the exposure even across the film plane.
A good tech should be able to detect the defect.
Yes, a test roll, shooting an even scene, would be quite revealing. And yes, do all speeds.
I'd be seeing about getting your seller to help pay for a shutter repair, since you haven't had it for long.
Vick