I have found that "homespun" varies from almost as loosely woven as bandage gauze (that's exagerating - but not by much) to about the same as "regulalar" quilting cotton.
I would also soak these fabrics in HOT water (after serging the edges) to get as much shrink in them as possible.
Then - as QuiltE suggested - use some sort of sizing/starch on the fabric BEFORE cutting it to help stabilize it.
An aside: I think one is supposed to starch/size the fabric - let it dry - and then dampen it? I know that I soaked a block with sizing - ironed/pressed it when sopping wet - and totally stretched/mutilated the poor block.
So - may want to check on the "proper" way to use sizing/starch.
I am in the "wash before cutting camp" - it just seems so much easier to not have to fret about what my fabrics may or may not do when they are washed.