How do I eliminate Corn Meal "grittiness"?
If you don't want gritty bread, use finely milled polenta. Roughly milled polenta is like semolina, and results in a gritty batter. Finely milled polenta is like flour, and results in a smooth batter. 

I don't know the proper names for the different milling grades in English. I don't mean cornflour, which is pure maize starch from the inside of the maize kernel. I mean whole maize kernels milled so the particles are the same size as wheat flour. It is yellow and tastes the same way as the rough one, only the texture is different. 

The two types of polenta differ in their water absorption and soaking times, so you may want to use a recipe developed for the fine milled type, or tweak your own recipe. 

To give you a better example, here is what you need: 



You don't want to use the rough form, which looks like this: