What about using a stiffener? Fusing either Annie's Soft n Stable or Lazy Girl's Stiff Stuff (it's thinner) on the outer blocks to keep the points straight and then you could sew a regular sleeve behind the 3 black blocks on the top.
I have used the Stiff Stuff to make a small basket. It is stiff enough to hold the points, but it is flexible enough to lay flat or fold.