I spend a little extra and get really fine ground corn.
I use a heated sonic cleaner about $50 dollars on line. (2 five minute cycles, with Dawn dishwashing detergent, vinegar and some salt) Run it through the tumbler. Because of the cleaner I rarely have to change my media. Deprime, size, trim and tumble it again. Then load and I am ready to rock.
YMMV
If you decap first you can use either compressed air, or one of those "canned air" products for cleaning computers to blow the contents out. Put the air in through the primer pocket and since you have may have resized the neck when you decapped it should be that much easier to get the corncobs out.
I've had this issue with any media I use on necked down cases. I make it a habit of tapping my cases a few times on the inside of the tumbler lid when removing it to empty the case of any media and rarely have issues with medi remaining in the case after that.
Of course, straight cases, such as for handguns, never present this problem.