I don't do paper piecing either. I also don't care much for starching.
But I've done stratas before by pressing freezer paper on the back of the whole already sewn strata strip; then cut out the shapes -- especially if the edges of the shapes will be on a bias (like diamonds). I sew the shapes together with a short stitch length; crease the paper along the seam line; run my awl along the crease on the paper; then peel the paper off easily.
Jan in VA