This bag turned out closer to my vision. I knit it on a smaller gauge loom with more pegs, and kept the color stripes clean. I liked the color contrast edging I added to the blue bag, so included that in the knitting process. Here's the bag after it came off the loom, and the bottom seam was sewn. I was a little concerned with the rolling of the bound off edge, but it turned out not to be a problem. There is definite biasing again. I rarely have that problem when knitting in the round, so I'll attribute it to the twist of the yarn.
This time I felted it with just a pair of tennis shoes in a small load on the heavy duty cycle. I checked it after 5 minutes, and the felting was well on its way, but still had distinct columns of knitting. After 5 more minutes, it seemed just right, though a bit small. I let it go through the rinse and spin cycles.
Orville Redenbacher came to the rescue this time. That box is slightly bigger than the Cream of Wheat box I used on the blue bag. I had to stretch the bag a little to get it to fit, which was fine. The corners of the box were helpful to remove the biasing of the knitting.
And here is the finished bag, with the button-tab closure and real handles. I would have liked it to be a little wider, and the tab could be longer, but I'm still pleased with it.
The original piece of knitting was 11" x 11". The finished bag is 7" x 7", with a 3" bottom. Again, the knitting shrank more side to side than it did top to bottom.