Or, like Andy said, you can file and sand away the inner portion of the grille, making it more like a 1:1 grille. There would be no need to paint the recesses black if they're not there,
Here are a couple of pics of a 55 Chevy on which I filed away the back of the grille.
On this shot, you can see just a glimpse of silver from one of the fan motors on the front of the radiator.
From the top, you can better see how I filed away the entire back of the grille, leaving just the "eggcrate" front portion.
It's just another option to explore; I hope you found the information helpful.
David G.