I know this is an old post, but will answer for the sake of others who may ask. :)
I had the exact same problem two years ago. Here in FL, we usually grow our veggies and sunflowers in winter months, to avoid the bugs.
But two years ago, my sunflowers were behind and made it into June, hence the arrival of the hated beetles that eat the big black holes into the sunflower heads. I was picking them off by groups of 3 and 4 at a walk-by, and 3 or 4 times a day!!!
I found that placing some of my old panty hose over the flower heads and knotting them in the back allowed the head to continue to grow and stop the beetles.
As far as use, just pick a thumb's width circle of the surrounding seeds that were where the attack took place, and use them for the birds. The rest of the head is perfectly fine for human use. I hope this helps future sunflower gardeners. Those pantyhose sure stopped my frustration! :)