Leah I love the hexagon projects, they just go anywhere as a "Drag Along" project. I have made the flowers (either three or four rows around - counting the center one) and then appliqued them onto a 8" or 10" square. Goes so much quicker, looks lovely and it takes 110 squares for a queen sized bed. Sometimes I applique the flowers onto the square, or if for a child, I use my machine to button-hole-stitch them onto the block. Instead of using the paper patterns, check out "Brandi's" and order the reusable templates from her. You can starch and press over the template and then when cool, remove them by cutting the stitches. I do the whole flower before starching and removing the templates.
Good luck and have fun. Consider fussy-cutting some of the pieces, especially for the center one.