heirloom sunflower variety for seed oil

I am gradually transforming a 11 acre conventional sunflower-wheat plot into a mixed permaculture- market garden - demonstration plot project. It will take couple more years for the process to be complete. Meanwhile I have to learn how to grow wheat and sunflower. It is fun to see how some increase in organic matter content and mineral balancing does to production.
Here is the problem I am facing right now. Sunflower seeds -hybrids- are way too expensive over here. So much expensive that, it almost costs as much as all other inputs. So I did what was expected of me and tried to stabilize f1 sunflower. Then I hit to a rock wall. Unlike wheat - which even F2's perform well,  F1 sunflower seeds are like tomatoes - F2's has nothing to do with F1. Million heads, some tiny flowers some massive flowers. Stalks way too thin or way to thick - some look like Boa trees.

I have been searching for heirloom sunflower seeds for seed oil production. Not the ones for bird feed, not the ones for eating, but for seed oil. While it was easy to find heirloom wheat varieties it has been extremely difficult to pinpoint a single heirloom that was used for seed oil in say 1950. Am I missing something? Why are all varieties for seed oil production F1's? Is there anyone selling old varieties?

I know there will be some loss of production per acre and also oil percentage, but cost saved from buying expensive seed each year should help with the math.

Thanks!

When we planted sunflowers it was black oil seed sunflowers.

Unfortunately the deer got all of them.

Thanks! So it seems like there is the black oil seed sunflower and that is it's name. It is one stem and single headed.

While searching I came across Peredovik oil seed sunflower which is poly headed (southern exposure seed exchange). It seems strange that there is like 150 heirloom corn variety for flour,but just few oil seed sunflower.