Smack, after all this, I still don't see why anybody would include lying ahull in their repertoire. It's known to be uncomfortable (at a time when you really need to eat or sleep) and dangerous. There are two alternatives (stick with step 2 if you're confident your sails can take it, or move on to step 4), each of which is more attractive than lying ahull. So why ever do it?
I agree with you, AL. I don't see a big advantage - and Roth certainly doesn't seem to advocate it very strongly, especially with more modern boats, even though it is one of his steps. He lists a whole lot of "ifs" in that chapter and stresses the need for predictable seas. He has this sentence as its only real justification:
Remember that our little game in a strong wind is to play for time and a change in the weather. With luck, after 4 or 5 hours of lying a hull, the storm may decrease and move off.
So what you say above about sticking with 2, then moving to 4 is exactly what Jeanne seemed to be doing, with the intent to run just long enough to deploy the JSD - and it makes a lot of sense, especially in sketchy seas like those she was in.
I think you could also argue that waiting to the point that you're moving too fast while running under bare poles has its dangers as well, making an earlier deployment of the JSD an attractive (and conservative) option.