I tried to felt the strap more by felting in the kitchen sink, agitating with a wooden spoon, and alternating between very hot water and cold water to shock the fibers. This had absolutely no effect. I also tried ironing. Nada.
Then, last night, inspiration struck. If I simply cut the felted fabric, could I re-felt it by needle felting? I retrieved my felted swatches and cut them up. First, I tried abutting the cut edges and needle felting them back together by aiming the needle in at an angle. This worked sort of okay, but it was dangerous to use the barbed needles this way (even on the foam pad) and didn't result in the strongest join. Next I tried overlapping the cut edges by about 3/8" and felting perpendicular to the strap, from both the top and the bottom. Voila! It worked! So I grabbed the bag, cut about 17" off the strap, and proceeded to jab it with the felting needles until it was attached again. I started to work on the lining and hope to make more headway on that today. In the end, the bag isn't as big as we intended, but it's not far off. Also, the flap isn't rectangular. The corners are kind of swoopy. I wonder if it would have held the rectangular shape better if I put an i-cord binding around the edge, or something like that? Would that have stabilized it?
Every time I do a felting project like this, I want to felt everything I see. I have a healthy stash of felting yarn now and am itching to make more bags. I know, I need another bag like I need another hole in my head... but there are some cute ones out there. That reminds me... last Christmas, one of the books I received was The Knitter's Book of Yarn (LOVE IT) and the Calla Lily bag caught my eye (Ravel it). Hmmm. Another project on the to-do list?