I wouldn't hesitate to use spray starch, but since you will be using so much, consider doing it outside. You don't need to freeze the clothes. You are not pressing it to remove wrinkles but to contain the threads once you have clipped. This will help with control until your quilt is quilted.
I struggle with certain kinds of homespun for the same reason and contrary to other posters, this stuff was never washed. Same problem with the fabric I got from Connecting Threads. That stuff frayed HORRIBLY and I almost threw the stuff out. I decided to prewash and all the fraying stopped. So, it very well could be just the fabric and the reason why some have no problem with it without washing is because of stabilizers added by the manufacturer.
I have bought Mary Ellen's Best Press clear starch alternative, but as I haven't used it yet, I can't recommend it. Again, since you will be using so much, spray outside if you can. Inhaling anything you spray is generally not good for the lungs.