I am happy to say that I worked with the pile of scrappy strips that I shared yesterday.
Last night I sewed a few strip sets.
Here is a picture of the back of the original cozies that I made. This shows that I sewed a few "extra" lines on those from what is suggested on the instructions. I really like adding the stitching that creates a square along what will be the bottom of the cozy. I feel like it helps them stand more upright. Honestly, you can quilt as much or as little as you like. It doesn't matter. You can even use decorative stitches, if you want. You are the decision maker here. :-)
So...here is my scrappy bowl cozy. I like it and have enough strip sets sewn to make at least two more. I am also going to make a couple of the large cozies. That strip set will measure approximately 17" x 17" and be trimmed to 16" square. I'll follow the same procedure, including using the large pre-cut batting.