I am also a dedicated pre-washer, but I think the quilting world is divided 50-50, so you are in good company! A rule of thumb is either pre wash everything or nothing. The non-prewashers say that if there's enough quilting, the top is stabilized and any shrinkage won't be noticeable.
Do not wash the cut pieces, they will not be usable for your project.
I would totally complete one of your 3 quilts (piece top, sandwich, quilt and bind), then wash. Then you can decide which camp you will go with.
The only exception is flannel. That you probably should always wash twice, it can continue to shrink.
Last edited by PaperPrincess; 11-16-2014 at 09:19 AM.