You can cut oversize templates of the units in the PP block. I am surprised that you posted you have done Judy Niemeyer and were not familiar with this technique. All of her patterns call for making an oversized template that matches the shape of the piece in her pattern. It simplifies the process of PP, conserves fabric and in some cases ensures the outer edge of the completed unit is on the grain. It would be very easy to do on your crossed canoe block.
Geri B, the popularity of PP is to achieve nice sharp points of odd angles that are not as easily done with more traditional piecing methods.