I have had similar rattles before, not entirely sure how one appeared. The first bit I had rattle was one of the slides that allows the lift arm to raise and lower the window (has the plastic insert that moves horizontally). Perhaps the previous owners had the window replaced at some time. It was really random to find an extra piece hiding in the bottom of the door frame.
Also, I have had a rattle due to having a rocker panel coming loose. Albiet this was a more plastic rattle, it was just a clip that pulled loose. A firm press and it was reattached.
However, my passenger door has a similar rattle at what you describe now, perhaps padding or travel stops. Did you ever solve the problem?