I have heard many discussions on pros and cons of washing vintage quilts. Here is a link that gives you some good advise I hope.
http://www.quilthistory.com/cleaning.htm
Would you ever consider separating the blocks and working them individually into a new block such as a snowball with a red and white print? That would result in stabilizing a fragile fabric and providing square corners. Also new machine piecing would be stronger. Then you could test color fastness of each block. It is entirely possible that some of the redwork is colorfast and other pieces are not. You could then use also use a very fine fusable to attach the red work to a preshrunk muslin or use a very lightweight fusable interfacing before re-piecing.