I wouldn't cut down all the blocks. I like Tanya's idea. It will add a bit of mystery to the quilt. Don't remember who wrote it but I read an article a while back about make-do quilts. They're quilts with one or two pieces that are different in some way. She collects them.
Edited: I found the link. Check this out.
http://www.heartspunquilts.com/make-do-primer.htm