This started out as "light" version of Jim Talbot's method to flatten a face and apply a decal but it's already running long...
Episode 1 is on Youtube. How to flatten a face?
errata: at about 5:35 you can see a bit of distortion happening on the screen-left edge of the mesh. That is because those patches are right next to the hidden stretched patches. Those will decal oddly at that edge. Ideally we would have one more column of patches between those and the stretched patches to