I wonder if running your cornmeal (dry) through a blender for a couple of minutes might break it down a little? Like when you want finer sugar.
In theory it's possible. However, not all blenders are created equal. This link mentions doing it, but in my experience to blend something into a super fine powder (a flour-like consistency) you need a really powerful machine like a Vita-mix. Also you may get inconsistencies in texture with a blender. This is one reason professional coffee bars use burr grinders instead of blade grinders: to achieve a consistent grind.