This was an interesting problem. On the surface it seems easy; however, as you consider the options as modeler and texture artist, complications arise.
As I hopefully make clear in this tutorial, this is a question of trade offs. We can create rectangular strips that are easy to paint on and very nicely fill the UV space. However, they will contain UV stretching or compression distortions.
Or we can remove the distortions but have oddly shaped UV shells to paint on. The end result will probably look much better at the cost of the effort required to paint on it.
After I posted this to my YouTube channel; I thought of a possible hybrid solution. I may experiment with that over the weekend and write about it here if it bears useful fruit.