In that case, just avoid taking a Yamanote line train before 9am, as the bulk of morning commuters must be in their offices by then.

When I have a bulky suitcase, I aim for the frontmost/rearmost door on Japanese commuter trains, as those have some more space next to the conductor's compartment, not to mention less passengers in the Yamanote line's case (not too many station exits at the ends of platforms).