I have been reading Debra Wagner's Striplate Piecing book, and have come to the conclusion that starch is the key to the whole process. To quote: "On average, the fabrics I used...were starched to the stiffness of typing paper." She uses 3-4 coats of starch on her fabrics. "I am convinced that simply starching the fabric can double your piecing skills."
My take is that a foundation is needed for these detailed strips/blocks. It can either be an external skeleton like with the paper or freezer paper techniques, or an internal skeleton of heavy starch. With 3-4 coats of starch used the fabric doesn't stretch or wiggle, and the blocking becomes more of a double check for accuracy, rather than beating the fabric into submission.
I intended to try the Striplate technique again this month, but after starting with the freezer paper method I really got into the groove,and so kept going. It's slow, but mindless, and I really like the zen-like quality of the repetition. I may take some scrap fabric, starch the fool out of it, and piece one strip so I can report back to the group!