I can only tell you what works for me and perhaps that can make a difference for you, too. I drafted my own templates because I wanted a smaller block (6" ) than the ones in the book would have given me. I then traced the templates onto the fabric, both plain and stripped, and cut them out with scissors not a rotary cutter because of the thickness of the template plastic, as you have learned. :wink:
When piecing, I pin the heck out of the curves, L-shape on top, and sew slowly. Each piece that is cut from the strata, is actually bias cut so careful handling, even if you use heavy starch (which I do not), is critical. The odds of something stretching are very high, given the possibility of slightly off-grain strips plus bias edges.
Fast piecing does not really matter to me, accurate piecing does. I really enjoy working with color and value and Drunkard's Path is my favorite block, so the Strips 'n Curves was a natural for me.
This is one of my first attempts. It's called 'Blue Ridge Reverie'.