I'm not sure exactly what's going wrong there.
First don't add the cases to the media, until you have added your polishing agent and run the tumbler or vibrating machine for a while to disperse the polish. The stuff should feel dry when you add the cases. Too much of a good thing is bad.
Second, when you are done tumbling, dump the cases into a screen that will allow the media to fall through, yet stop the hulls. You can make your own, or buy them ready made.
Third, if the cases are still packed with media, put them back in the tumbler and run it for a while. The machine should knock the media from the cases. Once the media is falling out of the cases screen them again to remove and check to see if you need to repeat the tumbling.
I can't help but wonder if your media is damp or wet. The humid summer weather may have something to do with it. Maybe a short time in an oven at 200F would make it dry and flow easily. Keep it sealed from the air when storing.
I realize you may have already done all these things, I'm just suggesting what comes to mind. I also remember some type of ceramic media that was larger and wouldn't fit into a case mouth. Does anyone here remember the name of the stuff?
You can always expect a couple of chunks of media in a primer pocket or in the tiny vent hole. You will need to inspect each case.