What you want to look up is "winnowing". You can do it with just a big bowl and a bit of wind. Search for "sunflower winnowing".
Youtube has lots of videos with different techniques but most are fundamentally the same: shake a bowl of seed near the edge of the bowl and let the light ones fly out from the wind.
The process of removing the seed from the flower head is called threshing. For large fields, there are mechanical threshers. They're quite interesting to see in action!
I've had similar problems when I've grown just a few sunflowers by themselves. I guess there wasn't enough pollination going around. When I collect seeds for roasting I'm now growing multi-headed flowers nearby and a handful of the mammoths together. It's helped yield a lot.
If you're saving seed to regrow, don't mix varieties (so no small multiheaded sunflowers). Otherwise they hybridize and you lose the mammoth genes. You'll just have to grow more of them close together and hope they flower around the same time.
Hope you have better luck next year!