I would stablize the give or stretch with some starch prior to any cutting. The smaller stitch lenght used for paper peicing will help in the strenght of the seams.. I am a bit concerned about the raveling from using a loose weave fabric , I would opt for more dense quilting or if quilting on a regular machine quilting that is on the homespun rather than the denser weave fabric. WhenI have sewn/pieced homespuns I used a larger seam allowance, so maybe not trim as close , and that would resolve the issues. .. but I would still starch prior.
FYI - its looks beautiful so far.