I got out the heirloom white spray paint, gave them two good coats after removing the glass and backing, and they looked fantastic! They looked like I had just bought them at a store. Perfect! I wanted them to have a different look and texture than normal picture frames and mats, so I found two of my favorite pictures - one of my mom as a young woman dancing in a short dress, and one of my dad curled up as a baby on my grandma's lap. I centered them on the material and cut out an appropriate size box from fabric squares, making the fabric the mat.
I then put the frames back together and I was very happy with the results: