You can definitely take out one side and add to the bottom. I would do this a block at a time.
I don't understand how the batting is. Is there a backing fabric? Was the chicken scratch done through the top fabric and the batting?
Edit: Oh, I just saw your other post and photo of the back. It does look as if the chicken scratch was done through batting. I think what I would do, after changing the block arrangement, is simply add a backing fabric and hand or machine sew over all the block seam lines. The chicken scratch is already enough "quilting" to hold the batting together to the top fabric. I would just be very careful when washing and drying the quilt, and would also be sure the backing fabric is pre-shrunk before layering.
Lovely old quilt!
Last edited by Prism99; 06-23-2012 at 09:12 AM.