I would do the applique first, then sandwich, baste, and quilt. Most of my quilts are donated, so although I prefer cotton batting, I use poly, I have yet to pre-wash my cotton batting and have never had a problem by "bumpies", which actually I think is more prevalent in poly batting. Although you say you think cotton batting is "too warm", I consider it just the opposite, cotton batting "breathes" since it's a natural product, whereas poly batting does not.