I ordered the disolving applique paper that Sharon Schamber uses and I've seen her do very tiny stems using it. I could use that for the weave strips so the edges are finished and straight then glue down the back of each strip, leaving the ends free. Maybe do it on a thin muslin background.
After doing the weave use the Piece-lique technique to sew the green triangle onto the end of each strip. I would be able to mark where each triangle goes and place it perfectly for sewing. Then glue all the ends down and sew around the edges.
Going to need to do some test pieces to see what works.