I got a response about good sunflowers to grow from someone on GardenWeb who grows a lot of cutting flowers. Here’s what he said:

Autumn Beauty mix from Johnny’s has been our mainstay for years. I also plant Jokers and maybe 1 or 2 for fun each season. And, also Sunbrights – which are our “big” sunflowers. Of course the Autumn Beauties make quite a tall “hedge” in the garden but the flowers aren’t enormous.

I already bought some sunflower seeds for this year, but maybe I’ll try these next year.