I would definitely use the spray starch to stabilise the fabrics, but test it first. I've never had a problem on fabric - the iron yes, fabric no.
When doing the Poppins return bag, I sewed the strips onto a base, I only used interfacing on the most frayey of the fabric. In my case because it was a bag the fabric I used was quite stiff, but you could use a lightweight fabric, and then a lightweight lining.
It's a bit like the quilt as you go method, but means your shapes stay very stable.
Jessie