Well, the dremmel's the cleanest way of doing it. I ran into this problem before David posted about the issue. I just used a pocket knife and wittled away at the plastic until the cable fit snugly. Of course, I had just bought a new cable for patching on my way to a show, so I didn't really have much time to come up with an "elegant" solution.
You could always find a short patch cable that fits fine without having to remove some of the plastic, and always use that plugged into the JB3. Even just a short female->male connector would work, though I've never seen one for 1/8" miniplug. Other than that, I don't see any way around this.