Upload & Sell: On
In normal circumstances, the 300/4L IS does jump a bit, and it clunks and grinds a bit too, but it doesn't make nearly as large a difference in framing as your example shows. Also, it doesn't cause the image to go OOF. Sounds like it's time for a trip to a Canon service centre.
The 300/4L IS will "drift" when on a tripod, as it's first gen IS doesn't recognize when it's in a stable condition, and so it ends up integrating noise in the motion sensors; otherwise, it's pretty solid, when it's working right.