I was right, painting the individual strips on the scarf made more work for myself.
Using the method describe in Hi-Fi Color, I create a selection mask from the flat colors. This way I can make changes to the painting, but still select the individual items as needed. This means that if I wish to paint a section of the Doctor's scarf, I have to select each individual strip. It also means that I have to clean up the selection because the areas between the flat colors are not perfect. Therefore each time I paint the scarf, I am spending an extra minute or two cleaning up the area I will be painting.
I would have continued to work around this mistake, but then I made two additional mistakes.
The first mistake that I made was taking a short cut. Instead of hand painting the texture of the scarf, I was going to use a image of a knit that I had available. Now the Doctor's scarf does not lay flat. It wraps around his body two or three times. It is rolled up on itself. It's even folded. With all of these shapes, I should have realized that I needed to hand paint the texture. I could have recovered from this, but then I made my second mistake.
I was not saving incremental files.
I work as a programmer, and I am very familiar with version control. The rule is that once you get a section working, save it to the version control system. The reason is simple. It gives you the ability to go back to a earlier version. What I should have done was save a new file when the flats were complete, and then again when the hat was complete. If I had done that, I could have back to the version that had the completed hat. Now I have to clean up the mess that I made before I can go forward again.
Hopefully, I'll learn from my mistakes.