If you can get the quilt to the shape of the box, put it in a plastic garbage bag and then suck the air out of it, with a vac attachment, to shrink it. I did this when we mailed 150 rag dolls to my son in Baghad for the children at the medical unit he worked at.
(USPS also charges by size,since we couldn't use priority boxes, we tried to keep the sizes down.)
You guys are doing a great job!