I am just finishing up a small pillow with only 16 puffs. It is the second one that I have made. I wanted to try one last year because my high school graduation quilt made by my grandmother was a puff quilt using worn out nylon stockings for the puff fillers. It was HEAVY.
Anyway, dealing with filled puffs when sewing is a challenge, so I do as much sewing as possible when the puffs are empty. I sew my puffs with the right side facing out to a muslin backing putting the pleats all the way around using a 1/8" seam. I pin and sew one side at a time chain piecing with the other puffs rather than sewing around all 4 sides of a puff before moving on. For me it makes pleating easier, since it is hard for me to pleat while the puff is under the presser foot.
When all puffs are made, I make the slits in the muslin for later stuffing and sew the puffs together using a 1/4" seam. The top is then sewn onto the backing in preparation for the birthing, but before turning, I stuff the puffs and do a quick hand sewing of the slit together on each one. It doesn't have to look pretty, since it is on the inside.
Because I am making pillows, I do a two piece quilted back fastened by Velcro. The large Velcro opening makes the birthing easy.
I am trying to get up the energy to do a baby quilt, because I know they are popular. However, those puffs are very tedious, and I would have to reserve half the winter for the project! The quilt my grandmother made is twin size with small puffs. The puffs are machine sewn on 3 sides turned and hand sewn on the 4th side, as well as hand sewn to the other puffs. There is no backing. It was a labor of love from Grandma to be sure!
Good luck with your project -- I hope you will post a picture when finished.