Harvesting Garden Sunflower Seeds for Birds?

What's the most practical method to harvest sunflower seeds? As pedals dry out, I cut off the heads leaving enough stem to hang in groups to dry or finish maturing. After a month or so, the seeds are "thumbed out" of the head leaving behind flying seeds and sore thumbs. Short of machinery (this is just a garden border harvest) is there a simpler and less painful way to save the winter feed for the birds?

By Dick Mc