Nice pattern and I love your fabrics! I've only done 1 paper piecing, but loved it and bought a couple more patterns (including this one)! I would think for that pattern it would be quicker if you cut the pieces similar size to what you need and then line them up assembly line style. You can always use the scraps to do another project!
I did see somewhere that instead of getting up frequently to iron, they used a little roller like you use on the seams when wallpapering. I haven't tried that, but I bet it would save me time running back and forth as my ironing board is across the room from my sewing machine.
Keep us posted with pics! :)