I finally found a (semi)free program for extracting files from an iPhone backup. I used it to grab all of my images from an old backup, including some from an app (camera+). I don't remember the name of the software off the top of my head, but I can post it later when I have access to my computer. Most of the "free" software packages I tried wanted money to recover more than a few images, but this one did them all for free. I recovered hundreds of images that I thought I had lost.
I don't know how to get your backup files down from the cloud though. Mine were already on my computer.