I wish I had a picture of the Tshirt quilt I made a couple of years ago - the picture is in CT, and I'm in AZ. Anyway, the point is that I fused a fusible kniw facing to the back of the Tshirts to stabilize them before sewing them into the quilt. I used bigger pieces of the shirts than just the logos, so they definitely needed the stabilizing.
Blue Chicken - your quilt is gorgeous, and my prayers are with your nephew. Having gone through the cancer journey myself, my emotions and memories come roaring back whenever I hear about someone else being diagnosed. It's especially heartrending when a young person is sent on that journey. I'll cheer when I hear he's 'officially' in remission!