Oh my. Fraying is indeed a problem. Yes, starch helps, and now they are cut out you could line several up, spray starch and press.
Having said that, do you want to do all the work of making a quilt and have it come apart. I had one baby quilt that just came apart, and I wished I had just junked the fabric. I knew that there was a problem but kept going, and wished I had not.
If you decide to continue, I would recommend dense quilting.
amh