Deborah, I like the Flower Beds pattern. I think it would work well. (Just so you know, you could make the quilt I made without making strips. In the first one, which is hard to see, some of the "strips" are made up of smaller pieces sewn together, and not all of the strips are 1/2 inch wide. I made that one out of scraps of all sizes when our guild had "grab bags" for us to take and create charity quilts from. All I had was a stack of very strange sized pieces of fabric. I sewed them together randomly...not really strips, and then cut them into 10 inch squares. I had to use my own white fabric for stashing, but that was allowed for that particular challenge.)
I was reading about scrappy quilts on another thread, and it sent me to quilterscache.com, to a pattern called Sunny Lanes. I don't think that pattern is what you are looking for, but it might be. I intend to make one like it, I think.
However, I like the Flower Beds pattern too. I may have to make it too.
Enjoy the process, whatever you decide...and I know your grandmother will love it!
Dina