I found a Youtube video by Ph2 with a flower base that was near identical to a number of other flower petal turnings I have done before. Squash then squash then squash and you get 16 petals per flower – nice. Using a simpler form the sepal works. Having the basis for the fold I set about selecting paper and scale to make these things near actual size.
I countered the negative curvature of the sepal with the positive curvature of the back of the flower with (shhhh) a little craft glue, made stems and fleshy leaves (as per roses), then inserted stems into convenient slots in the now affixed sepals and presto – sunflowers.
It turns out that YES, you can make lovely sunflowers out of paper – who knew?