Lori, have you considered making pillows instead? I would think that would be easier and you could leave a frayed edge outside of the stitching, like a rag quilt. That way, you could stitch the edges first and cut second. I haven't made pillows, myself, but if you use a form, that sounds a lot easier than dealing with a quilt. The sweater should adhere to the form nicely while you're making it. Plus, it would be huggable. You might try that while you're experimenting.
hugs,
Charlotte